The perimeter of the rectangle is double that of the area of the square. Find the length of the rectangle.

30 cm

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37 cm

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25 cm

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10 cm

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Solution

The correct option is B 37 cm

It is given that the side of the square is 7 cm.

Hence, area of the square = 7 × 7 = 49 sq cm

Given:
Length of the rectangle = (5x + 7) cm

Width of the rectangle = 2x cm

∴ Perimeter of the rectangle
= 2(2x + 5x + 7)
= 14x + 14

Hence, we have:

14x + 14 = 2 × 49

⇒ 14x = 98 – 14 = 84 [Subtracting 14 from both sides]

⇒ x = 6 [Dividing by 14 on both sides]

So, the length of the rectangle
= 5x + 7
= 5 × 6 + 7
= 37 cm

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