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?

16 cm
18 cm
24 cm
Data inadequate

Correct answer: 18 cm

Solution

Given $\frac{P}{b}=5$, we have $P=5b$. Since $P=2(l+b)$, it follows that $2(l+b)=5b$, so $2l=3b$ and $l=\frac{3}{2}b$. Using area $lb=216$, we get $\frac{3}{2}b^2=216$, hence $b=12$ and $l=18$ cm.

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