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math area

by sumasajja » Sat Jul 23, 2011 8:21 am
a rectangular rug covers half of a rectangular floor that is 9ft wide and 12 ft long.If the dimensions of the rug are in the same ratio as those of the floor,how many ft long is the rug?
a] 6
b] 21/2
c] 2 root 7
d]6 root 2
e]4 root 6
the answer is d
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by goalevan » Sat Jul 23, 2011 9:20 am
A rug covers half of a rectangular floor whose area is 9 * 12 = 108, so the area of the rug will be 108 / 2 = 54.

We are given that the room's length is 12 and its width is 9, so the ratio of length to width is 12/9 = 4/3.

The dimensions of the rug must be in the same ratio, so

L/W = 4/3, 3L = 4W and W = (3/4)L

L * W = L * [(3/4)L] = 54, so L^2 = 54(4/3)

L^2 = (54/3)*4 = 18*4 = 72 = 2*2*2*3*3, so L = 2 * 3 * sqrt(2) = 6 root 2.
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by MBA.Aspirant » Sat Jul 23, 2011 10:57 am
sumasajja wrote:a rectangular rug covers half of a rectangular floor that is 9ft wide and 12 ft long.If the dimensions of the rug are in the same ratio as those of the floor,how many ft long is the rug?
a] 6
b] 21/2
c] 2 root 7
d]6 root 2
e]4 root 6
the answer is d
floor area = 9*12 = 108

area of rug = 54

rug l and w are in ratio 12:9 or 4:3

4x*3x = 54

12x^2 = 54

x = 3/√2 = 3√2/2


length = 4* 3√2/2 = 6√2
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