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# What is the perimeter, in meters, of a rectangular playground 24 meter

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Math Expert
Joined: 02 Sep 2009
Posts: 46284
What is the perimeter, in meters, of a rectangular playground 24 meter [#permalink]

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20 Sep 2017, 01:55
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76% (00:42) correct 24% (00:57) wrong based on 25 sessions

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What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?

(A) 112
(B) 152
(C) 224
(D) 256
(E) 304

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Re: What is the perimeter, in meters, of a rectangular playground 24 meter [#permalink]

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20 Sep 2017, 05:18
Bunuel wrote:
What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?

(A) 112
(B) 152
(C) 224
(D) 256
(E) 304

Equating the Areas of the two rectangular playgrounds = 64x48=l x 24
l = 128 m
Perimeter = 2x(128+24)
=304m

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What is the perimeter, in meters, of a rectangular playground 24 meter [#permalink]

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20 Sep 2017, 06:38
Bunuel wrote:
What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?

(A) 112
(B) 152
(C) 224
(D) 256
(E) 304

Find area of first playground to find its perimeter.

For area of the first playground, use the doubling and halving rule to find the length of the first rectangular playground.*

Areas of the two playgrounds are equal:

$$(24)(L_1) = (48)(64)$$

W = 24 is half of W = 48. If one factor is halved, the other is doubled. $$L_1 = (2*64) = 128$$. OR

$$L_1 = \frac{(48)(64)}{24} = (64 * 2) = 128$$

Perimeter of first playground: 2(24 + 128) = 304

*You could also factor to avoid long calculations:

$$(24)(L_1) = (48)(64)$$
$$[(3)(8)](L_1) = [(6)(8)][(8)(8)]$$
Factor out 8 on both sides. Isolate L on LHS by dividing 6 by 3 = 2. Then L = (2)(8)(8) = 128
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What is the perimeter, in meters, of a rectangular playground 24 meter   [#permalink] 20 Sep 2017, 06:38
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