The perimeter of a square and an equilateral triangle are equal. If the length of side of equilateral triangle is 4 cm more than that of the square, then find the perimeter of the square.

16 cm

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36 cm

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48 cm

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12 cm

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Solution

The correct option is C 48 cm
$Let the length of the side of square be x c m .$

$Then, the length of side of the triangle is (x + 4) c m .$

The perimeter of the square is 4x cm.
The perimeter of the equilateral triangle
= (x + 4) + (x + 4) + (x +4)
= 3(x+4) cm

$According to the question, \Rightarrow 4 x = 3 (x + 4) \Rightarrow 4 x = 3 x + 12 \Rightarrow 4 x - 3 x = 12 \Rightarrow x = 12$

So, the length of the side of the square is 12 cm.

Perimeter of the square
$= 4 \times 12 = 48 c m$

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