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Bunuel
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Bunuel
A certain rectangle has perimeter 54. If the ratio of the length of the rectangle to the width is 5 : 4, what is the length of the rectangle?

(A) 30
(B) 27
(C) 24
(D) 18
(E) 15


We can express the ratio as L : W = 5x : 4x

The perimeter of a rectangle is 2L + 2W = P, so we can create the equation:

2(5x) + 2(4x) = 54

10x + 8x = 54

18x = 54

x = 3

Therefore, the length of the rectangle is 5 * 3 = 15.

Answer: E
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Another approach.. Substitution method:
2(L+B) = 54
=> L+B=27.......Eq 01

L/B=5/4 => B=4L/5

Substituting B=4L/5 in Eq..01
L + 4L/5 = 27 => 9L =27 x 5 = > L=3 (hit Kudos if you didnt think of this method :) )
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