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# If a square mirror has a 20-inch diagonal, what is the

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Manager
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If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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Updated on: 07 Dec 2012, 05:56
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If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 120

My aprroach is;

$$20= X \sqrt{2}$$

then $$X=10\sqrt{2}$$

$$4*X \sqrt{2} = 45,6$$

so should i round it to 40 or 60?

Originally posted by fatihaysu on 18 Aug 2010, 07:44.
Last edited by Bunuel on 07 Dec 2012, 05:56, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 62637
Re: Look easy but something wrong  [#permalink]

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18 Aug 2010, 07:57
4
3
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?

You made an error in calculation: $$P=4*10\sqrt{2}\approx{56.6}$$ ($$\sqrt{2}\approx{1.4}$$), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.
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Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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01 Sep 2013, 11:39
6
1
fatihaysu wrote:
If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 120

My aprroach is;

$$20= X \sqrt{2}$$

then $$X=10\sqrt{2}$$

$$4*X \sqrt{2} = 45,6$$

so should i round it to 40 or 60?
.

Here is my approach, i think it will be very simple and do not need any calculations.
if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
##### General Discussion
Manager
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Re: Look easy but something wrong  [#permalink]

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18 Aug 2010, 07:59
1
Bunuel wrote:
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?

You made an error in calculation: $$P=4*10\sqrt{2}\approx{56.6}$$ ($$\sqrt{2}\approx{1.4}$$), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.

It is definelty clear Bunuel. I am triped up by not remembering it is 1,14 or 1,4.

thank you
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If a square mirror has a 20-inch diagonal, what is the approxima  [#permalink]

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26 Oct 2012, 01:50
memorize the fact that diagonal of a square with side s = s * root ( 2)

u ll get the answer half a min
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Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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09 May 2013, 18:31
I'm I doing the last step correctly?

$$10\sqrt{2}$$ = 10 x 1.4 = 14 right, therefore 14x4 = 56.

Thanks.
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Joined: 02 Sep 2009
Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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10 May 2013, 00:12
laythesmack23 wrote:
I'm I doing the last step correctly?

$$10\sqrt{2}$$ = 10 x 1.4 = 14 right, therefore 14x4 = 56.

Thanks.

Yes, that's correct.
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If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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28 May 2015, 05:25
Question:

Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!
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Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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28 May 2015, 05:28
noTh1ng wrote:
Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!

$$\frac{20}{\sqrt{2}}=\frac{20*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=10\sqrt{2}$$.
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If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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Updated on: 28 May 2015, 05:46
Bunuel wrote:
noTh1ng wrote:
Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!

$$\frac{20}{\sqrt{2}}=\frac{20*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=10\sqrt{2}$$.

Thank you Bunuel the calculation is clear, but I just don't get why we do that?!extending?

Why isn't 20 / sqrt2 sufficient?

Originally posted by noTh1ng on 28 May 2015, 05:35.
Last edited by noTh1ng on 28 May 2015, 05:46, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 62637
Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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28 May 2015, 05:42
noTh1ng wrote:
Bunuel wrote:
noTh1ng wrote:
Diagonal of a square = x * sqrt2

20 = x * sqrt2
x = 20 / sqrt2

Why are you all using x = 10 / sqrt2 ? I got to the same result with 20 / sqrt2 as length of one side, but where is my mistake?

Thanks!!

$$\frac{20}{\sqrt{2}}=\frac{20*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=10\sqrt{2}$$.

Thank you Bunuel the calculation is clear, but I just don't get why we do that?!

Because $$10\sqrt{2}$$ is considered to be more simplified (rationalized) than $$\frac{20}{\sqrt{2}}$$.

This algebraic manipulation is called rationalization and is performed to eliminate irrational expression in the denominator.

Questions involving rationalization to practice:
if-x-0-then-106291.html
if-n-is-positive-which-of-the-following-is-equal-to-31236.html
in-the-diagram-not-drawn-to-scale-sector-pq-is-a-quarter-139282.html
in-the-diagram-what-is-the-value-of-x-129962.html
the-perimeter-of-a-right-isoscles-triangle-is-127049.html
which-of-the-following-is-equal-to-98531.html
if-x-is-positive-then-1-root-x-1-root-x-163491.html
1-2-sqrt3-64378.html

Hope it helps.
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Schools: WHU MBA"20 (A$) GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: If a square mirror has a 20-inch diagonal, what is the [#permalink] ### Show Tags 07 Jul 2015, 09:01 The diagonal of a square splits it in 2 right triangles --> the area of one traingle = (B*H)/2 = 100 (Height is 50% of the diagonal) So the square have an area of 2*100=200 which is almost 14^2 ----> 4*14 = 56 nearest to 60 (B) CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 3476 Location: India GMAT: QUANT EXPERT Schools: IIM (A) GMAT 1: 750 Q51 V41 WE: Education (Education) Re: If a square mirror has a 20-inch diagonal, what is the [#permalink] ### Show Tags 07 Jul 2015, 14:09 3 fatihaysu wrote: If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches? (A) 40 (B) 60 (C) 80 (D) 100 (E) 120 If the Square has side = $$x$$ then the diagonal of Square = $$x\sqrt{2}$$ i.e. $$x\sqrt{2} = 20$$ i.e. $$x = 20/\sqrt{2} = 10\sqrt{2}$$ Perimeter = 4*Side = $$4*x = 4*10\sqrt{2}$$ i.e. Perimeter = $$40\sqrt{2}$$ = $$40*1.4 = 56$$inch Answer: Option B _________________ Prosper!!! GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi Click Here for Uneditable GOOGLE reviews Click here for Our VERBAL & QUANT private tutoring package details My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION Intern Joined: 05 Sep 2015 Posts: 1 Re: If a square mirror has a 20-inch diagonal, what is the [#permalink] ### Show Tags 05 Sep 2015, 09:04 Can somebody solve this with Trigonometry. Thank you. CEO Joined: 20 Mar 2014 Posts: 2543 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: If a square mirror has a 20-inch diagonal, what is the [#permalink] ### Show Tags 05 Sep 2015, 10:37 merwalpiyush19 wrote: Can somebody solve this with Trigonometry. Thank you. Sure, look below. If you draw the diagonal in a square, it will divide the square into 2 congruent triangles such that the diagonal makes $$45^{\circ}$$ with the sides. Consider, triangle ABC, $$\frac{AB}{AC}$$ = sin ($$\angle {ABC}$$) = sin (45) = $$\frac{1}{\sqrt{2}}$$ , where AC =20 Thus, AB = $$\frac{20}{\sqrt{2}}$$ = $$\frac{20*\sqrt{2}}{2}$$= 10*$$\sqrt{2}$$ = 10*1.4 = 14 Thus, the perimeter of the square = 4*AB = 4*14 =56. B is the closest answer Attachments 2015-09-05_14-34-36.jpg [ 9.97 KiB | Viewed 18134 times ] CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 3476 Location: India GMAT: QUANT EXPERT Schools: IIM (A) GMAT 1: 750 Q51 V41 WE: Education (Education) Re: If a square mirror has a 20-inch diagonal, what is the [#permalink] ### Show Tags 06 Sep 2015, 06:14 2 merwalpiyush19 wrote: Can somebody solve this with Trigonometry. Thank you. Since this question was pretty simple with Trigonometry as shown in the explanation above so my only curiosity is WHY do you want to know the solution of such question with Trigonometry when your base is already not strong enough in it? over an above that WHY trigonometry when this is not what GMAT ever expects from students? Writing here just out of concern so that other readers don't get influenced by Solutions by trigonometry as tool of solving such questions of GMAT. Please be careful while referring to the source of material, types of solutions etc. for GMAT preparation. If it's not what GMAT expects from you then It can only ruin your direction of healthy preparation. _________________ Prosper!!! GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi Click Here for Uneditable GOOGLE reviews Click here for Our VERBAL & QUANT private tutoring package details My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2801 Re: If a square mirror has a 20-inch diagonal, what is the [#permalink] ### Show Tags 09 Jun 2016, 13:09 3 fatihaysu wrote: If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches? (A) 40 (B) 60 (C) 80 (D) 100 (E) 120 We are given that a square has a 20-inch diagonal, and we must solve for the perimeter of the square. This means we first need to know the length of a side of the square. To determine the length of a side we can use the diagonal formula for a square. We know that: diagonal of a square = side√2 = s√2 20 = s√2 s = 20/√2 To help with our math we can multiply 20/√2 by √2/√2. This gives us: s = 20/√2 × √2/√2 = 20√2/√4 s = 20√2/2 = 10√2 We also should have memorized that the approximate value of √2 is 1.4. Thus one side of the square is about 10 x 1.4 = 14 inches. Finally, the perimeter of the square is 4 x 14 = 56. Since we are asked to approximate, the closest answer is 60. Answer B. _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 202 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Manager Joined: 06 Sep 2016 Posts: 122 Location: Italy Schools: EDHEC (A$)
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If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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04 Jul 2017, 06:44
I solved it using this reasoning:

When I know the diagonal I have to divide it by $$\sqrt{2}$$ to get the side.
I also know that $$\sqrt{2}$$ is something less than 2.

Consideration 1: 20/2 would be 10 so the perimeter would be 40
Consideration 2: If I assume that 20 is the side 20x4 gives me a perimeter of 80

So the answer must lie between 40 and 80... thus 60...
Clearly this only works because of the type of answer choices... but this is what GMAT often expects from us, right?
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Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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06 Apr 2018, 01:25
Bunuel wrote:
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?

You made an error in calculation: $$P=4*10\sqrt{2}\approx{56.6}$$ ($$\sqrt{2}\approx{1.4}$$), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.

Bunuel hello,

one question if one side of square is $$10\sqrt{2}$$ and perometr of square is 4a

shouldnt we have as an answer $$4$$ * $$10\sqrt{2}$$ = $$40\sqrt{2}$$
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Re: If a square mirror has a 20-inch diagonal, what is the  [#permalink]

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06 Apr 2018, 01:42
1
dave13 wrote:
Bunuel wrote:
fatihaysu wrote:
If a square mirror has a 20-inch diagonal,what is the approx. perimeter of the mirror,in inches?

a)40
b)60
c)80
d)100
e)120

My aprroach is;

20= X \sqrt{2}

then X=10\sqrt{2}

4*X \sqrt{2} = 45,6

so should i round it to 40 or 60?

You made an error in calculation: $$P=4*10\sqrt{2}\approx{56.6}$$($$\sqrt{2}\approx{1.4}$$), 56.6 is closer to 60 than to 40, thus answer is B.

If P were 45.6 (as you calculated) then the answer would be A, as 45.6 is closer to 40 than to 60.

Hope it's clear.

Bunuel hello,

one question if one side of square is $$10\sqrt{2}$$ and perometr of square is 4a

shouldnt we have as an answer $$4$$ * $$10\sqrt{2}$$ = $$40\sqrt{2}$$:?

You did not read carefully thus your question does not make sense.

From the solution you quote: $$P=4*10\sqrt{2}$$

Your question: "shouldnt we have as an answer $$4$$ * $$10\sqrt{2}$$ = $$40\sqrt{2}$$"

The SAME perimeter.
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Re: If a square mirror has a 20-inch diagonal, what is the   [#permalink] 06 Apr 2018, 01:42

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