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

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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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30 Nov 2015, 09:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

There are 2 variables (length:a, width:b), and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer.
Looking at the conditions together, ab=48, a^2+b^2=10^2=100, (a+b)^2-2ab=100, (a+b)^2=100+2ab=100+2*48=196, a+b=14 --> (a,b)=(6,8),(8,6), perimeter=2(6+8)=28
This is an unique answer, so is sufficient.

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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01 Dec 2015, 02:48

Let sides of rectangle are a & b. We need perimeter of rectangle i.e. P= 2(a+b)

Now statement 1 says: Diagonal length is 10, i.e. $$a^2 + b^2 = (10)^2$$
So, for $$(a+b)^2$$, we do not have value of 2ab. Therefore, insufficient

Statement 2 says: Area of rectangle is 48, i.e. a*b= 48.
Therefore 2*a*b= 96

but we do not have value of $$a^2 + b^2$$.
Therefore insufficient

Now combine 1 & 2,
We can find $$(a+b)^2$$, and thus Perimeter i.e. 2(a+b)
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If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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01 Dec 2015, 03:40
tsunagaru wrote:
Hi,

I am surprised as well that A was not the correct answer but not for the reasons explained in the previous posts (except if I missed something).

The question is stating that we have a rectangle to consider.

1) tells us that each diagonal of rectangle Q has length 10.

I would guess a rectangle that has its diagonals equal is always a square. If this is a square then knowing the hypotenuse (the diagonal) is enough to guess the perimeter.

Anyone to help me on this?
Thanks

If we knew the angles of the rectangle, then we might get an answer from question 1.

For example, if it was a square, then we would have a 90 - 45 - 45 triangle.
Or we could have a 90 - 60- 30 triangle (then this would not be a square).
As we don't know the angles, then we cannot deduce the lengths.

I did a different approach.
x*y = 48
48 = 2ˆ4 * 3
or... 2ˆ3 * 6 -> 8 * 6
So the lengths are 8 and 6, which is equal to the hypotenuse 10ˆ2.

Therefore letter C
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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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14 Jan 2017, 11:12
What is wrong with this approach? Please explain.

a²+b²=100 |√ on both sides
a + b = 10

P=2(a+b)=2*10=20

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Perim. of a triangle (DS question)  [#permalink]

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28 Feb 2017, 13:49
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'm extremely confused why the answer is C and not A. I thought that if you knew the diagonal of a rectangle to be one of the Pythagorean triples (3:4:5 in this case) you can assume the L & W to be 6 & 8? FYI, I understand why the answer is C if the triples logic is not applicable. Can someone please clarify? Thanks.

EDIT - Is the reason why you can't assume a 3:4:5 ratio is because you don't know whether the shape has equal or unequal sides i.e., square or not, and if you can use the 3:4:5 rule or the x:x:x sqrt(2) rule?
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Re: Perim. of a triangle (DS question)  [#permalink]

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28 Feb 2017, 13:56
v0latility 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'm extremely confused why the answer is C and not A. I thought that if you knew the diagonal of a rectangle to be one of the Pythagorean triples (3:4:5 in this case) you can assume the L & W to be 6 & 8? FYI, I understand why the answer is C if the triples logic is not applicable. Can someone please clarify? Thanks.

EDIT - Is the reason why you can't assume a 3:4:5 ratio is because you don't know whether the shape has equal or unequal sides i.e., square or not?

You can never assume a side ratio of a right triangle from only one side, whether or not it fits a special triangle ratio. You couldn't assume 3:4:5 even if we told you that the side length of the rectangle were unequal. It takes two sides to determine a right triangle.
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Re: Perim. of a triangle (DS question)  [#permalink]

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28 Feb 2017, 14:04
AnthonyRitz wrote:
v0latility 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'm extremely confused why the answer is C and not A. I thought that if you knew the diagonal of a rectangle to be one of the Pythagorean triples (3:4:5 in this case) you can assume the L & W to be 6 & 8? FYI, I understand why the answer is C if the triples logic is not applicable. Can someone please clarify? Thanks.

EDIT - Is the reason why you can't assume a 3:4:5 ratio is because you don't know whether the shape has equal or unequal sides i.e., square or not?

You can never assume a side ratio of a right triangle from only one side, whether or not it fits a special triangle ratio. You couldn't assume 3:4:5 even if we told you that the side length of the rectangle were unequal. It takes two sides to determine a right triangle.

Got it. Just want to understand this a little better - is the reason being that you don't have to use integers (e.g. the 3:4:5 ratio) to solve a^2 + b^2 = c^2?
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Re: Perim. of a triangle (DS question)  [#permalink]

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28 Feb 2017, 14:06
That's exactly right. There are infinitely many right triangles with hypotenuse 10. For instance, sqrt(13), sqrt(87), 10.
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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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12 Mar 2017, 21:13
So I answered this question using the Pythagorean Theorem...kudos for feedback- just want to make sure my technique and logic is consistent with correct mathematical principles.

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.

This question asks us to find the perimeter, denoted by p, of rectangle Q. That the perimeter is denoted by "p" is perhaps another GMAT trap meant to slow us down. Anyways, we need to know the width and the length.

Statement (1) tells us that the diagonal of rectangle Q is ten; though, this piece of information does not allow us to calculate the width or the length.

Statement (2) tells us that the area of rectangle Q is 48; albeit, there are multiple combinations of integers that satisfy the width and length ( 12 x 4, 8 x 6)

If we combine these statements we can see that ten corresponds to the 90 degree angle. 8 6 10 reduce to the pythagorean triplet 3 4 5 though I am not sure if this technique is really the best way of solving this question and somehow coincidentally works. Method > serendipity
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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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26 Mar 2018, 10:12

Solution:

Given:

• The perimeter of the rectangle Q = p

Working out:

We need to find out the value of p

Statement 1:

Each diagonal of the rectangle Q has length 10

Let us assume that the length of the rectangle Q is l, and the breadth of the rectangle Q is b.

From this statement, we can infer that $$\sqrt{l^2 + b^2}$$ = 10

• Squaring both the sides of the equation, we get $$l^2 + b^2 = 100$$

o There can be more than one possible combination of l and b.

o And hence, the sum of l and b is not unique.

Thus, Statement 1 alone is not sufficient to answer this question.

Statement 2:

Area of the rectangle Q is 48 units.

Let us assume that the length of the rectangle Q is l, and the breadth of the rectangle Q is b.

Thus, $$l*b = 48$$

There can be more than one combination of l and b: (6,8), (12, 4), etc. and the values of p will not be unique.

Thus, statement 2 alone is not sufficient to answer this question.

Combining both the statement:

From statement 1, we have $$l^2 + b^2 = 100$$

From statement 2, we have $$l*b = 48$$

• $$(l+b)^2 = l^2 + b^2 + 2l*b$$

• Or, $$(l+b)^2 = 100 + 96$$

• Or, $$(l+b)^2 = 196$$

• Or, $$(l+b) = 14$$ units.

From here, we can calculate the value of p.

Thus, combining both the statements, we got our answer.

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Re: If p is the perimeter of rectangle Q, what is the value of p &nbs [#permalink] 26 Mar 2018, 10:12

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