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# If the perimeter of a certain rectangle is 76 and its area is 360 then

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Joined: 02 Sep 2009
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If the perimeter of a certain rectangle is 76 and its area is 360 then  [#permalink]

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18 Jan 2018, 02:56
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15% (low)

Question Stats:

86% (01:59) correct 14% (02:58) wrong based on 37 sessions

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If the perimeter of a certain rectangle is 76 and its area is 360 then what is the length of its shortest side?

(A) 12
(B) 18
(C) 20
(D) 36
(E) 40

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Re: If the perimeter of a certain rectangle is 76 and its area is 360 then  [#permalink]

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18 Jan 2018, 05:36
Bunuel wrote:
If the perimeter of a certain rectangle is 76 and its area is 360 then what is the length of its shortest side?

(A) 12
(B) 18
(C) 20
(D) 36
(E) 40

Perimeter . = 2(l+b) = 76

i.e. l+b = 38

Area = l*b = 360

:et's think of two numbers whose sum is 38 and whose products is 360 (Instead of making a quadratic equation and creating more difficulty for ourselves)

The numbers are 18 and 20

Smaller side = 18

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Re: If the perimeter of a certain rectangle is 76 and its area is 360 then  [#permalink]

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18 Jan 2018, 05:44
I went about it as follows:
the shortest side is the largest when the rectangle with perimeter 76 is a square so:
76/4 = 19

meaning the answer for length a of the shortest side has to be a<19
--> A or B
A) if shortest side 12, then longest side is 26 (2x 12+ 2x 26 = 76)
B) if shortest side 18, then longest side is 20 (2x 18+ 2x 20 = 76)

12x26 = 312
18x20 = 360 --> B
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Re: If the perimeter of a certain rectangle is 76 and its area is 360 then  [#permalink]

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18 Jan 2018, 07:42
Bunuel wrote:
If the perimeter of a certain rectangle is 76 and its area is 360 then what is the length of its shortest side?

(A) 12
(B) 18
(C) 20
(D) 36
(E) 40

$$2 ( l + b ) = 76$$ & $$lb = 360$$

Or, $$l + b = 38$$ & $$lb = 360$$

Now check the options , within 10 sec U can come to the right answer (B) , as 18*20 = 360 & 18 + 20 = 38
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Re: If the perimeter of a certain rectangle is 76 and its area is 360 then  [#permalink]

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20 Jan 2018, 07:34
Bunuel wrote:
If the perimeter of a certain rectangle is 76 and its area is 360 then what is the length of its shortest side?

(A) 12
(B) 18
(C) 20
(D) 36
(E) 40

We can create the following two equations in which L = length and W = width:

2L + 2W = 76

L + W = 38

L = 38 - W

and

LW = 360

Substituting, we have:

(38 - W)W = 360

38W - W^2 = 360

W^2 - 38W + 360 = 0

(W - 20)(W - 18) = 0

W = 20 or W = 18

When W = 20, L = 18 and when W = 20, L = 18.

Thus, the shorter side is 18.

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Re: If the perimeter of a certain rectangle is 76 and its area is 360 then   [#permalink] 20 Jan 2018, 07:34
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