The sides of a rectangle whose area is 216 $c m^{2}$ are in the ratio 2:3. Find its perimeter.

60 cm

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30 cm

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6 cm

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5 cm

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Solution

The correct option is A 60 cm
Let the length and breadth of the rectangle be 2x and 3x respectively.

Area of rectangle = $l \times b$
$2 x \times 3 x = 216$
$6 x^{2} = 216$
$x^{2} = 216 \div 6$
$x^{2} = 36$
$x = 6 c m$

So, the sides of the given rectangle are
$l e n g t h (l) = 2 x = 2 \times 6 = 12 c m b r e a d t h (b) = 3 x = 3 \times 6 = 18 c m$

Now, perimeter of the rectangle
= $2 (l + b) = 2 (12 + 18) = 2 \times 30$

$∴$ Perimeter = 60 cm

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