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If the perimeter of a rectangular property is 46 meters, and the area

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If the perimeter of a rectangular property is 46 meters, and the area  [#permalink]

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New post Updated on: 25 Oct 2014, 06:48
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If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides?

A. 4
B. 6
C. 9
D. 18
E. 23

Originally posted by ojn on 10 Jul 2010, 16:27.
Last edited by Bunuel on 25 Oct 2014, 06:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If the perimeter of a rectangular property is 46 meters, and the area  [#permalink]

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New post 10 Jul 2010, 16:36
Welcome to GMAT Club!

The best way to solve this would be to backsolve - use the answer choices, so it is quite unfortunate that you did not provide them - that's the fastest way really.

Without answer choices, You would need to build an equation for Area and one for Perimeter such as:

A+ B+A+B = Perimeter
A*B = Area

So, A+B+A+B = 46
A*B = 76

Here we can do something like this:
2A+2B = 46 or A + B = 23 and thus A = 23-B

Plug that into the other equation: (23 - B)*B = 76 or 23B - \(B^2\) = 76
You have a quadratic equation to solve at this point:
\(-B^2 + 23B - 76 = 0\)

If you had answer choices, you could plug them in and see which ones worked but we can solve it as well (just picking numbers, looks like 4 works from positive roots).

So, the answers are: B = 4 and A = 19
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Re: If the perimeter of a rectangular property is 46 meters, and the area  [#permalink]

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New post 11 Jul 2010, 00:32
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bb's certainly right that we could have solved quicker using backsolving. If you had provided the answer choices, we could have also showed you how to use reasoning to quickly eliminate some of the choices.

Notice that the area is 76. The area is the product of the length and width. That is, the area is a multiple of each of the sides. So, each side is a factor of the area. So, the correct answer will be a factor of 76. You can quickly eliminate any choices that are not factors of 76.
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Re: If the perimeter of a rectangular property is 46 meters, and the area  [#permalink]

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New post 02 Dec 2015, 20:02
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Hi All,

While this question can be solved Algebraically, TESTing THE ANSWERS will work really quickly here.

We're told that the Perimeter of a rectangle = 46 and its Area = 76. We're asked for the length of the SHORTER side.

Since the area = 76, and (9)(9) = 81, the shorter side MUST be less than 9. This leaves us with Answers A and B. Since both the perimeter and area are integers, it is HIGHLY likely that both dimensions of the rectangle are also integers, so we should figure out what happens when we divide 76 by 6 and 76 by 4. Which of those options gives us an INTEGER?

76/6 = 12 2/3 which is NOT an integer.
76/4 = 19

If the sides were 4 and 19, then the perimeter would be 2(4) + 2(19) = 46. This is an exact MATCH for what we were told, so this MUST be the answer.

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Re: If the perimeter of a rectangular property is 46 meters, and the area  [#permalink]

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New post 02 Feb 2018, 12:25
ojn wrote:
If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides?

A. 4
B. 6
C. 9
D. 18
E. 23


We can let W = the width and L = the length and create the equations:

2W + 2L = 46

W + L = 23

L = 23 - W

and

WL = 76

Substituting, we have:

W(23 - W) = 76

23W - W^2 = 76

-W^2 + 23W - 76 = 0

W^2 - 23W + 76 = 0

(W - 4)(W - 19) = 0

W = 4 or W = 19

If W = 4, then L = 23 - 4 = 19.

If W = 19, then L = 23 - 19 = 4.

We see that the length of each of the shorter sides is 4.

Answer: A
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Re: If the perimeter of a rectangular property is 46 meters, and the area &nbs [#permalink] 02 Feb 2018, 12:25
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