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

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18 cm

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24 cm

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Data inadequate

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None of these

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Solution

The correct option is B
18 cm

$\frac{2 (l + b)}{b} = \frac{5}{1}$ $\Rightarrow$ 2l + 2b = 5b $\Rightarrow$ 3b = 2l $\Rightarrow$ b = $\frac{2}{3}$ l

Then, area = 216 cm $^{2}$ $\Rightarrow$ l $\times$ b = 216 $\Rightarrow$ l $\times$ $\frac{2}{3} l$ = 216 $\Rightarrow$ l $^{2}$ = 324 $\Rightarrow$ l = 18 cm.

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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?

The correct option is B 18 cm 2(l+b)b=51⇒ 2l + 2b = 5b ⇒ 3b = 2l ⇒ b = 23 l Then, area = 216 cm2 ⇒ l × b = 216 ⇒ l × 23l = 216 ⇒l2 = 324 ⇒ l = 18 cm.

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?