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1. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A. 16 cm

B. 18 cm

C. 24 cm

D. Data inadequate

Solution:

\begin{aligned} \frac{2 (l + b)}{b} = \frac{5}{1} \\ \Rightarrow 2 l + 2 b = 5 b \\ \Rightarrow 3 b = 2 l \\ b = \frac{2}{3} l \\ Then, \\ Area = 216 c m^{2} \\ \Rightarrow l \times b = 216 \\ \Rightarrow l \times \frac{2}{3} l = 216 \\ \Rightarrow l^{2} = 324 \\ l = 18 c m \end{aligned}

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