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20 Sep 2017, 01:55
Kudos
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E
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Difficulty:
25%
(medium)
Question Stats:
79% (01:14) correct
21%
(01:54)
wrong
based on 57
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
(A) 112
(B) 152
(C) 224
(D) 256
(E) 304
20 Sep 2017, 05:18
Kudos
Bookmarks
Bunuel
Equating the Areas of the two rectangular playgrounds = 64x48=l x 24
l = 128 m
Perimeter = 2x(128+24)
=304m
Answer E
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20 Sep 2017, 06:38
Kudos
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Bunuel
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
Answer E
*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
