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Rectangle Perimeter Area

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by EMAN » Mon Oct 05, 2009 5:57 pm
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

I could infer the correct answer but was a little rusty of how you would actually do it. Answers plus explanations for approaches would be greatly appreciated.
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Source: — Data Sufficiency |
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by umaa » Mon Oct 05, 2009 6:07 pm
IMO C.

I used the plug in method.

Statement 1:

We don't know the angle. So, not sufficient.

Statement 2:

There are so many choices.

Not sufficient.

Combining both, we'll get 6 and 8 as length and width.

OA?
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Correct

by EMAN » Mon Oct 05, 2009 6:48 pm
C is correct.

I won't even try to reproduce the unnecessary and long winded explanation the OG gives. Basically it sounds like it boils down to noticing that the diagonals of a rectangle are equal and that they form two right triangles. I think you could visualize these diagonals as the hypotenuse of each triangle. If you know that is 10 and the area is 48, then you know that a^2 + b^2 = 10^2 so they have to equal 8 and 6 in either order (64 + 36 = 100). From that, you could deduce the length by multiplying them by two I would think if you actually wanted to solve the problem (calculating the perimeter).
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by sanjana » Tue Oct 06, 2009 11:13 am
Given : Perimeter = p

We know Perimeter is 2(l+b)

Statement 1 :
Each diagonal has length 10

Hence,l^2+b^2=100

Cant find l or b so insufficient

Statement 2 :

lb=48
Again cannot find l or b so insufficient

Combining the 2 we have,
If we square the permiter ,
p^2=4(l+b)^2
=4*(l^2+b^2+2lb)
=4*(100+2*48)
=4*196
Therefore we can get p

Hence,C
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by hala0987 » Thu Apr 01, 2010 11:01 am
For this question i got A because automatically when you tell me the Diagonal is 10 which is the Hyp of a right angled triangle ..I'd know that it's a 6,8,10 Right Angled Triangle...Part B alone wouldn't help me ofcourse because i could get 12*4=48 but Part A to me is crystal clear because GMAT in many questions wants you to infer the triangle from the diagonal, i've seen it before...and if all you need is the perimeter then you dont need to know which is which , just add them and times it by 2
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by KICKGMATASS123 » Thu Apr 01, 2010 9:48 pm
hala0987 wrote:For this question i got A because automatically when you tell me the Diagonal is 10 which is the Hyp of a right angled triangle ..I'd know that it's a 6,8,10 Right Angled Triangle...Part B alone wouldn't help me ofcourse because i could get 12*4=48 but Part A to me is crystal clear because GMAT in many questions wants you to infer the triangle from the diagonal, i've seen it before...and if all you need is the perimeter then you dont need to know which is which , just add them and times it by 2
I got A for this question too. Just because we are supposed to know the special 3,4,5 = 90 degrees. here we know that the rectangle has a right angle and since we know the hyp we know that the other two sides are 8 and 6. we don't know which is length and which is width.. but that's alright.. since we just need to add the 2 sides. 2 (length + width) = perimeter!

therefore A
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by KICKGMATASS123 » Thu Apr 01, 2010 9:49 pm
hala0987 wrote:For this question i got A because automatically when you tell me the Diagonal is 10 which is the Hyp of a right angled triangle ..I'd know that it's a 6,8,10 Right Angled Triangle...Part B alone wouldn't help me ofcourse because i could get 12*4=48 but Part A to me is crystal clear because GMAT in many questions wants you to infer the triangle from the diagonal, i've seen it before...and if all you need is the perimeter then you dont need to know which is which , just add them and times it by 2
I got A for this question too. Just because we are supposed to know the special 3,4,5 = 90 degrees. here we know that the rectangle has a right angle and since we know the hyp we know that the other two sides are 8 and 6. we don't know which is length and which is width.. but that's alright.. since we just need to add the 2 sides. 2 (length + width) = perimeter!

therefore A
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by dream700 » Fri Apr 02, 2010 2:19 am
guys, just coz hyp is 10 doesnt mean that the sides has to be 6 and 8... nowhere it is mentioned that the sides value are integers...so if i take value of a as anything i ll get the corresponding value of b...hence insuff

C is the answe
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by sanju09 » Fri Apr 02, 2010 2:43 am
EMAN wrote: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

I could infer the correct answer but was a little rusty of how you would actually do it. Answers plus explanations for approaches would be greatly appreciated.
For the perimeter of a rectangle, all we need is the sum of its flanking sides; let's call it p + q.

(1) Each diagonal would then be sqrrt (p^2 + q^2) = 10 (as per the on hand account), which cannot give p + q uniquely. Insufficient

(2) Area of rectangle would then be p q = 48 (as per the on hand account), which cannot uniquely determine the values of p and q, and hence cannot give p + q uniquely. Insufficient

Taken together...

We know that all measurements here are non-negative, and that p + q = ±sqrrt (p^2 + q^2 + 2 p q), perimeter can be determined uniquely now. TS [spoiler](Together Sufficient)

C[/spoiler]
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by sanju09 » Fri Apr 02, 2010 3:15 am
umaa wrote:IMO C.

I used the plug in method.

Statement 1:

We don't know the angle. So, not sufficient.

Statement 2:

There are so many choices.

Not sufficient.

Combining both, we'll get 6 and 8 as length and width.

OA?
Why do you need angle umaa, and which angle would you like to have so that perimeter can be found?

Dear hala0987 & KICKGMATASS123,

Data Sufficiency section on GMAT is the trickiest in the entire test. It wants deductions rather than assumptions. We must know and understand the dictionary's explanation for the two different words, deduction and assumption. Assumptions are never safe on GMAT and Deduction is the KEY to GMAT. There is no ambiguity in the wordings that the GMAT provides, so the wordings are to be taken as true to its all logically applicable meanings called DEDUCTIONS, and hence anything beyond that logical freedom is illogical or ASSUMPTION. Consider this example, if you ever find on GMAT, reading:

You are my real brother but I am not your real brother.

ASSUMPTION: This statement is definitely inconsistent.

DEDUCTION: You are my real brother but I am not your real brother because I am your real sister.
The mind is everything. What you think you become. -Lord Buddha



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by evangelia » Wed May 05, 2010 9:04 am
Although the OA is C. I think the answer should be C.
You cannot find another a pair of X, Y which meet the equation X^2+Y2=100. The only pair of X, Y should be 6 & 8.
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by evangelia » Wed May 05, 2010 9:05 am
Although the OA is C. I think the answer should be A.
You cannot find another a pair of X, Y which meet the equation X^2+Y^2=100. The only pair of X, Y should be 6 & 8.
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by ssuarezo » Wed May 05, 2010 9:47 am
EMAN wrote: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

I could infer the correct answer but was a little rusty of how you would actually do it. Answers plus explanations for approaches would be greatly appreciated.
Hi:

From stm1: According to pitagoras, if 10 is the diagonal of a right triangle, there no other possible measure than 6, 8 as the sides of the triangle, that s why they are special right triangles, the triangle is a 3,4,5 form.

From Stm2: it could be 24*2, 12*4, not suff.

An expert reply please !
Silvia
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by gmatmachoman » Wed May 05, 2010 10:32 am
ssuarezo wrote:
EMAN wrote: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

I could infer the correct answer but was a little rusty of how you would actually do it. Answers plus explanations for approaches would be greatly appreciated.
Hi:

From stm1: According to pitagoras, if 10 is the diagonal of a right triangle, there no other possible measure than 6, 8 as the sides of the triangle, that s why they are special right triangles, the triangle is a 3,4,5 form.

From Stm2: it could be 24*2, 12*4, not suff.

An expert reply please !
Silvia
Ok coming to ur query, what if the other 2 sides are like sqrt(99) & 1.

Still u get hypotunesue to be 10. So we can have many number of pairs to make 10.

Your assumption would have been logical provided all the sides need to be Integers. (6,8, 10) makes sense!

So pick C!!
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