GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2019, 08:24 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If a right triangle has area 28 and hypotenuse 12, what is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Retired Moderator Status: The last round
Joined: 18 Jun 2009
Posts: 1195
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34 If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

3
12 00:00

Difficulty:   45% (medium)

Question Stats: 75% (02:15) correct 25% (02:47) wrong based on 228 sessions

### HideShow timer Statistics

If a right triangle has area 28 and hypotenuse 12, what is its perimeter?

A. 20
B. 24
C. 28
D. 32
E. 36

_________________

Originally posted by Hussain15 on 13 Jun 2010, 05:04.
Last edited by Bunuel on 26 Dec 2013, 03:47, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 57022
Re: Doubtful PS  [#permalink]

### Show Tags

4
2
Hussain15 wrote:
If a right triangle has area 28 and hypotenuse 12, what is its perimeter?

A. 20
B. 24
C. 28
D. 32
E. 36

Let the legs of this right triangle be $$x$$ and $$y$$.

Given: $$area=\frac{xy}{2}=28$$ --> $$xy=56$$ and $$hypotenuse=x^2+y^2=12^2$$.
Question: $$P=x+y+12=?$$, so we should calculate the value of $$x+y$$.

Square $$x+y$$ --> $$(x+y)^2=x^2+2xy+y^2$$. As $$xy=56$$ and $$x^2+y^2=12^2$$, then: $$(x+y)^2=x^2+2xy+y^2=12^2+2*56=256$$ --> $$x+y=\sqrt{256}=16$$.

$$P=x+y+12=16+12=28$$.

Answer: C.
_________________
##### General Discussion
Senior Manager  Joined: 30 Aug 2009
Posts: 255
Location: India
Concentration: General Management
Re: Doubtful PS  [#permalink]

### Show Tags

2
2
Hussain15 wrote:
If a right triangle has area 28 and hypotenuse 12, what is its perimeter?

A. 20
B. 24
C. 28
D. 32
E. 36

C - 28
let the other 2 sides be a and b then we have 1/2 * a*b = 28 or a*b =56
also we have a^2 + b^2 = 144

adding 2ab to a^2 + b^2 we have a^2 + b^2 + 2ab = 144 + 2*56 = 256 => (a+b)^2 = 256 or a+ b = 16. So perimeter is a+b+ hypotenuse = 16+ 12 = 28
Retired Moderator Status: The last round
Joined: 18 Jun 2009
Posts: 1195
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34 Re: Doubtful PS  [#permalink]

### Show Tags

1
xy=56 & x+y=16,, what will be the values of x & y??

Posted from my mobile device
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 57022
Re: Doubtful PS  [#permalink]

### Show Tags

Hussain15 wrote:
xy=56 & x+y=16,, what will be the values of x & y??

Posted from my mobile device

We have the final answer without calculating the exact values of $$x$$ and $$y$$. So it doesn't matter. But if you are interested:

$$xy=56$$ and $$x+y=16$$, $$y=16-x$$:

$$x(16-x)=56$$ --> $$x^2-16x+56=0$$ --> $$x=8-2\sqrt{2}$$ and $$y=16-x=8+2\sqrt{2}$$ OR $$x=8+2\sqrt{2}$$ and $$y=16-x=8-2\sqrt{2}$$.

Hope it helps.
_________________
Retired Moderator Status: The last round
Joined: 18 Jun 2009
Posts: 1195
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34 Re: Doubtful PS  [#permalink]

### Show Tags

Thanks Bunuel!! Actually I started to solve this problem by using 3 4 5 formula of right triangle I.e 3^2+4^2= 5^2.This ended no where!! Posted from my mobile device
_________________
Intern  Joined: 25 Mar 2010
Posts: 1
Re: Doubtful PS  [#permalink]

### Show Tags

Apologies

Can someone explain why we are adding 2ab?

I don't understand that part.

Cheers
Retired Moderator Joined: 20 Dec 2010
Posts: 1717
Re: Doubtful PS  [#permalink]

### Show Tags

1
k4lnamja wrote:
Apologies

Can someone explain why we are adding 2ab?

I don't understand that part.

Cheers

No need to be apologetic k4lnamja. You can ask any question so far it's related to the topic.

We are dealing with a right angle triangle;

We are given its area and the hypotenuse and we are asked for perimeter.

Right angle triangle has three sides; one of which is hypotenuse. If we know the length of the other two, we will have the perimeter. However, there is no way to find out the length of the other two sides individually. Thus, our intention is to find the combined length of the other two sides and add it up with the hypotenuse to get the perimeter.

How can we use the information to know the combined length of the other two sides. Here's how.

Hypotenuse = c = 12
Let the other two sides of the right angle triangle be "a" and "b" and we know these two sides are perpendicular to each other.

Area = 28
Area of a triangle = 1/2*base*height = 1/2*a*b

1/2*a*b=28
a*b=56
c=12

As per pythagoras:
a^2+b^2=c^2
(a+b)^2-2ab=c^2
(a+b)^2-2*56=12^2
(a+b)^2-112=144
(a+b)^2=256
a+b=16

Thus, we know the sum of other two sides.
a+b=16
c=12
a+b+c=16+12=28
******************

Ans: "C"

**********************
Just to expand the formula used:
(a+b)^2=a^2+b^2+2ab
(a+b)^2-2ab=a^2+b^2
(a+b)^2-2ab=c^2
**********************
_________________
Director  Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 941
Re: Doubtful PS  [#permalink]

### Show Tags

1
1/2 * 12 * altitude = 28
altitude = 7

using similar triangle

7/x = x/12 gives x^2 = 84

12^2 - 84 = 60

thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.

Hence C.
Director  Joined: 01 Feb 2011
Posts: 624
Re: Doubtful PS  [#permalink]

### Show Tags

area = (1/2)bh = 28 => bh=56

hypotenuse = sqrt(b^2+h^2) = 12 => b^2+h^2 = 144

perimeter = b+h+sqrt(b^2+h^2)

we know that (b+h)^2 = b^2+h^2+2bh

= 144+2(56)

=> b+h = 16

=> perimeter = 16+12 = 28
Manager  Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

amit2k9 wrote:
1/2 * 12 * altitude = 28
altitude = 7

using similar triangle

7/x = x/12 gives x^2 = 84

12^2 - 84 = 60

thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.

Hence C.

I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.

Thanks! _________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps Math Expert V
Joined: 02 Sep 2009
Posts: 57022
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28
altitude = 7

using similar triangle

7/x = x/12 gives x^2 = 84

12^2 - 84 = 60

thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.

Hence C.

I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.

Thanks! Cross-multiply $$\frac{7}{x} = \frac{x}{12}$$ to get $$7*12=x*x$$ --> $$84=x^2$$.
_________________
Manager  Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

Bunuel wrote:
DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28
altitude = 7

using similar triangle

7/x = x/12 gives x^2 = 84

12^2 - 84 = 60

thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.

Hence C.

I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.

Thanks! Cross-multiply $$\frac{7}{x} = \frac{x}{12}$$ to get $$7*12=x*x$$ --> $$84=x^2$$.

Hi Bunuel,

Thanks for the very quick reply. I understand the calculation, just not sure about how we use similar triangles to arrive at that line in the first place? Don't understand why we are doing $$\frac{7}{x} = \frac{x}{12}$$ in the first place... Sorry if this seems rudimentary... _________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28
altitude = 7

using similar triangle

7/x = x/12 gives x^2 = 84

12^2 - 84 = 60

thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.

Hence C.

I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.

Thanks! I believe Bunuel has answered your question.

As a matter of fact, the text in red above is incorrect. The altitude should be 14/3 and NOT 7 as it has been calculated. The final answer as well is an integer, dont know how is the poster getting a decimal value.

IMO, the method is a 'forced' one as I am having difficulty in coming to the same equation for 'x'. Not a good method.
Manager  Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

Engr2012 wrote:
DropBear wrote:
amit2k9 wrote:
1/2 * 12 * altitude = 28
altitude = 7

using similar triangle

7/x = x/12 gives x^2 = 84

12^2 - 84 = 60

thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.

Hence C.

I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base.

Thanks! I believe Bunuel has answered your question.

As a matter of fact, the text in red above is incorrect. The altitude should be 14/3 and NOT 7 as it has been calculated. The final answer as well is an integer, dont know how is the poster getting a decimal value.

IMO, the method is a 'forced' one as I am having difficulty in coming to the same equation for 'x'. Not a good method.

I completely overlooked that part in red, in that case 1/2 * 12 * altitude = 28 altitude = 4 2/3. However I will take your advice and leave this one alone as I don't want to confuse myself.

Edit: Edited 4 3/2 to 4 2/3

_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps Originally posted by DropBear on 16 Aug 2015, 18:50.
Last edited by DropBear on 16 Aug 2015, 19:48, edited 1 time in total.
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

DropBear wrote:

I completely overlooked that part in red, in that case 1/2 * 12 * altitude = 28 altitude = 4 3/2. However I will take your advice and leave this one alone as I don't want to confuse myself.

I believe you meant 4 2/3 instead of 4 3/2
Manager  Status: 2 months to go
Joined: 11 Oct 2015
Posts: 107
GMAT 1: 730 Q49 V40 GPA: 3.8
If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

1

Another approach:

GMAT loves special triangles and guess what this is a special triangle.

With an hypotenuse of 12, the first thing that comes to my mind is a 30:60:90 triangle (l:l√3:2l),

If this was the case, we would have:
2l= 12
l=6
l√3= 6√3

To test it we simply apply the pythagorean theorem, $$6^{2}+\left( 6\sqrt{3} \right)^{2}\; has\; to\; equal\; 12^{2}\; ->\; \sqrt{36\; +\; 108}\; =\; \sqrt{144}\; ->\; 12\; =\; 12\;$$

$$->\; The\; right\; triangle\; is\; a\; 30:60:90\; triangle.$$

Now that we know the measures of the sides we simply add them.
2p= 12+6*1,7 +6= 12 + 5*2 + 6 = 28.

Answer C.
Intern  Joined: 06 Apr 2013
Posts: 2
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

1
what is wrong with this approach?

(1/2)*b*h=28
b*h = 56
now 56 can be broken down into following pairs
1, 56
2, 28
4, 14
8, 7
Since two sides of a triangle must be bigger than third side we can use 8,7 so the perimeter is 8+7+12=27
BUT 8^2 + 7^2 does not equal 144.

Where did I get it wrong??
Math Expert V
Joined: 02 Sep 2009
Posts: 57022
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

1
digitalmohsin wrote:
what is wrong with this approach?

(1/2)*b*h=28
b*h = 56
now 56 can be broken down into following pairs
1, 56
2, 28
4, 14
8, 7
Since two sides of a triangle must be bigger than third side we can use 8,7 so the perimeter is 8+7+12=27
BUT 8^2 + 7^2 does not equal 144.

Where did I get it wrong??

We are not told that the legs have integer lengths, so bh = 56 does not mean that b and h must be the values you consider.
_________________
Manager  B
Joined: 20 Apr 2019
Posts: 81
Re: If a right triangle has area 28 and hypotenuse 12, what is  [#permalink]

### Show Tags

Bunuel wrote:
Hussain15 wrote:
If a right triangle has area 28 and hypotenuse 12, what is its perimeter?

A. 20
B. 24
C. 28
D. 32
E. 36

Let the legs of this right triangle be $$x$$ and $$y$$.

Given: $$area=\frac{xy}{2}=28$$ --> $$xy=56$$ and $$hypotenuse=x^2+y^2=12^2$$.
Question: $$P=x+y+12=?$$, so we should calculate the value of $$x+y$$.

Square $$x+y$$ --> $$(x+y)^2=x^2+2xy+y^2$$. As $$xy=56$$ and $$x^2+y^2=12^2$$, then: $$(x+y)^2=x^2+2xy+y^2=12^2+2*56=256$$ --> $$x+y=\sqrt{256}=16$$.

$$P=x+y+12=16+12=28$$.

Answer: C.

How do we know that one leg of the triangle must be the height? Re: If a right triangle has area 28 and hypotenuse 12, what is   [#permalink] 14 Aug 2019, 04:55

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by

# If a right triangle has area 28 and hypotenuse 12, what is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  