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

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

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28 Feb 2017, 15:06
1
That's exactly right. There are infinitely many right triangles with hypotenuse 10. For instance, sqrt(13), sqrt(87), 10.
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If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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23 Nov 2017, 07:53
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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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09 Dec 2017, 06:47
i chose answer A since this is a rectangle and the diagonal will bisect the right angles, forming 45-45-90 triangle with sides ratios of 1:1:root 2.
using Pythagorean theory , we can get the value of both sides

what did i do wrong here ?
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If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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09 Dec 2017, 06:54
mohamk wrote:
i chose answer A since this is a rectangle and the diagonal will bisect the right angles, forming 45-45-90 triangle with sides ratios of 1:1:root 2.
using Pythagorean theory , we can get the value of both sides

what did i do wrong here ?

The diagonals of a rectangle bisect the angle if and only the rectangle is a square. Generally, a diagonal of a rectangle can form any angle with the adjacent sides from 0 to 90, not inclusive.
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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, 11:12

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  [#permalink]

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17 Jul 2019, 22:21
So for those who couldn't follow Bunuel's explanation, hopefully this helps:

So the key to this problem is to know that with just the area alone you can not find the perimeter. Since 48 can be broken into several ways (12x4) & (8x6). Only when we are told that the diagonal is 10 can we determine that 6-8-10 triangle is the only way that the area 48 and diagonal 10 makes sense. So now together (C) is correct and we know that the side is 6-8-10 and the perimeter is 2(8)+2(6)=28.
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Re: If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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13 Sep 2019, 06:31
L^2+2LW+W^2=(L+W)^2
100+2*48=(L+W)^2
14=L+W
48=L*W

Two distinctive equations, two variables.
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If p is the perimeter of rectangle Q, what is the value of p  [#permalink]

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08 Oct 2019, 23:54
Bunuel wrote:
SOLUTION

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.

Just to understand it better (open question for everyone)
OFC now that I see the solution it makes totally sense, but what is the logical approach in seeing/ thinking that one needs to square the (P) to arrive at a sufficient solution?

I tried tons of other steps, for example a two equation system but would never come up with this solution.

These kind of solutions are also typically the ones that are not teached in standard textbooks or school / university math.

Is this just pure number sense and logic?
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If p is the perimeter of rectangle Q, what is the value of p   [#permalink] 08 Oct 2019, 23:54

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