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

 It is currently 19 Oct 2018, 15:08

### 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

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

# If the perimeter of rectangle Q - Confused about simple Q

Author Message
Manager
Joined: 20 Oct 2011
Posts: 117
Concentration: Sustainability, General Management
GMAT 1: 710 Q49 V38
GPA: 3.98
If the perimeter of rectangle Q - Confused about simple Q  [#permalink]

### Show Tags

19 Nov 2011, 13:28
00:00

Difficulty:

25% (medium)

Question Stats:

87% (00:45) correct 13% (01:20) wrong based on 52 sessions

### HideShow timer Statistics

If p is the perimeter of rectangle Q, what is the value of p ?

(1) Each diagonal of rectangle Q has length 10.
(2) The area of rectangle Q is 48.

Now, the obvious choice is [spoiler=]C
, but I figured that is the trap answer and I guessed . Isn't it true that the hypotenuse of a right angled triangle, if 10, will have sides 6-8? Or is this not always the case? I know that if the triangle is not Right angled, then it is not the case;

but here: if the diagonal is 10, and since it is a rectangle, the 2 sides should be 6-8 and thus we can find the perimeter. Of course this is the same answer that you get by substituting values and using 2).

But OA says that we cannot know the sides from 1) or 2) and thus we need 1) and 2).

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-p-is-the-perimeter-of-rectangle-q-what-is-the-value-of-p-135832.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Senior Manager
Joined: 28 Jul 2011
Posts: 370
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: If the perimeter of rectangle Q - Confused about simple Q  [#permalink]

### Show Tags

19 Nov 2011, 13:38
+1 C

from 1 we only know about the diagonal lenght and e do not get any information of sided so 1 not sufficient,

From two we know area 2*l*b=48 but l and b can have various values i.e for example 8*6 or12*4 so we cannot get exact values of l and B so 2 not sufficient

Now combining 1 and 2 we get area and diagonal i.e hypotenuse so now solving

we now know that diagonal which has lenght=10 and with two sides of the rectangle form a right angled triangle, and so when you consider above l or B values it only satifies for 8 and 6 or 6 and 8 as 6-8-10 form a right angle traingle, and now we know l and B values so you can find perimeter which is 2(l+B)

Hope this clarifies
_________________

Manager
Joined: 20 Oct 2011
Posts: 117
Concentration: Sustainability, General Management
GMAT 1: 710 Q49 V38
GPA: 3.98
Re: If the perimeter of rectangle Q - Confused about simple Q  [#permalink]

### Show Tags

19 Nov 2011, 13:57
kotela wrote:
+1 C

from 1 we only know about the diagonal lenght and e do not get any information of sided so 1 not sufficient,

From two we know area 2*l*b=48 but l and b can have various values i.e for example 8*6 or12*4 so we cannot get exact values of l and B so 2 not sufficient

Now combining 1 and 2 we get area and diagonal i.e hypotenuse so now solving

we now know that diagonal which has lenght=10 and with two sides of the rectangle form a right angled triangle, and so when you consider above l or B values it only satifies for 8 and 6 or 6 and 8 as 6-8-10 form a right angle traingle, and now we know l and B values so you can find perimeter which is 2(l+B)

Hope this clarifies

Thanks. I understand how to solve it.

My question was simply that, if a right angled triangle is given with a hypotenuse 5 or 10 for instance; can we not automatically assume that it is a 3-4-5 or a 6-8-10 triangle? I suppose you can make fractional values to satisfy this.

Nevermind, I just realized my mistake. I was doing another difficult question earlier where I came across a situation like this, but it was on a coordinate plane, and each value "HAD" to be an integer. Hence with a hypotenuse of 10, the only values for the 2 sides could have been 6 and 8. But I suppose if the integer condition is not specified, then the 2 sides of the right triangle can take any values.

Ok, yea the answer is fine as given. Doh!
Director
Joined: 03 Sep 2006
Posts: 803
Re: If the perimeter of rectangle Q - Confused about simple Q  [#permalink]

### Show Tags

20 Nov 2011, 01:51
alinomoto wrote:
This is from the OG12, but I am confused about something:

48. If p is the perimeter of rectangle Q, what is the value of p ?

(1) Each diagonal of rectangle Q has length 10.
(2) The area of rectangle Q is 48.

Now, the obvious choice is , but I figured that is the trap answer and I guessed . Isn't it true that the hypotenuse of a right angled triangle, if 10, will have sides 6-8? Or is this not always the case? I know that if the triangle is not Right angled, then it is not the case;

but here: if the diagonal is 10, and since it is a rectangle, the 2 sides should be 6-8 and thus we can find the perimeter. Of course this is the same answer that you get by substituting values and using 2).

But OA says that we cannot know the sides from 1) or 2) and thus we need 1) and 2).

Given:
$$2*(l+b)=p$$
S1: $$l^2+b^2=10^2$$ (Pythagoras theorem) With this, we can't even solve l and b, so no chance of getting the p.

S2:$$l*b=48$$. With this, we can't even solve l and b, so no chance of getting the p.

What we need to solve is p, which is

$$p=2*(l+b)$$
Note that $$(l+b)^2=l^2+b^2+2*l*b$$

Using S1 and S2:
$$(l+b)^2=10^2+2*48$$,
Thus $$(l+b)$$ can be found.

Which means $$p$$ can be found.

Therefore the answer should be "C"
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: If the perimeter of rectangle Q - Confused about simple Q  [#permalink]

### Show Tags

23 Nov 2017, 07:53
If p is the perimeter of rectangle Q, what is the value of p?

Question: $$P=2(a+b)=?$$

(1) Each diagonal of rectangle Q has length 10. $$d^2=a^2+b^2=100$$. Not sufficient.
(2) The area of rectangle Q is 48. $$ab=48$$. Not sufficient.

(1)+(2) Square P --> $$P^2=4(a^2+b^2+2ab)$$. Now as from (1) $$a^2+b^2=100$$ and from (2) $$ab=48$$, then $$P^2=4(a^2+b^2+2ab)=4(100+2*48)=4*196$$ --> $$P=\sqrt{4*196}=2*14=28$$. Sufficient.

Similar questions to practice:
http://gmatclub.com/forum/if-the-diagon ... 04205.html
http://gmatclub.com/forum/what-is-the-a ... 05414.html
http://gmatclub.com/forum/what-is-the-p ... 96381.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-p-is-the-perimeter-of-rectangle-q-what-is-the-value-of-p-135832.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: If the perimeter of rectangle Q - Confused about simple Q &nbs [#permalink] 23 Nov 2017, 07:53
Display posts from previous: Sort by