Discussion
The ratio between the perimeter and breadth of a rectangle is 5:1. If the area of the rectangle is 216 sq. cm, then the length of the rectangle is
Answer: A
The length is 18 cm.
Let the length be \(l\) and the breadth \(b\). The perimeter is five times the breadth:
\[ \begin{aligned} 2(l + b) &= 5b \Rightarrow l = 1.5b \\ l \times b &= 1.5b^{2} = 216 \\ b^{2} &= 144,\ b = 12 \end{aligned} \]
So \(l = 18\) cm. Check: the perimeter is \(2(18 + 12) = 60\) cm, and 60 : 12 = 5 : 1. 24 cm would need a breadth of 9 cm, which gives a perimeter ratio of 66 : 9, not 5 : 1.
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