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

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

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