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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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New post 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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New post 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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New post 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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New post 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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New post 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.

Answer: Option 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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New post 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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New post 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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New post 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.

Answer: C.

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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