Mathematics
A rectangle has twice the area of a square. The length of the rectangle is 12 cm greater and the width is 8 cm greater than a side of a square. Find the perimeter of the square.
Answer
Let length of a side of a square = x cm.
According to question,
Length of rectangle = (x + 12) cm
Breadth of rectangle = (x + 8) cm
Given,
⇒ Area of rectangle = 2 × area of square
⇒ (x + 12)(x + 8) = 2 × (x × x)
⇒ x(x + 8) + 12(x + 8) = 2x2
⇒ x2 + 8x + 12x + 96 = 2x2
⇒ x2 – 2x2 + 8x + 12x + 96 = 0
⇒ -x2 + 20x + 96 = 0
⇒ x2 – 20x – 96 = 0
⇒ x2 – 24x + 4x – 96 = 0
⇒ x(x - 24) + 4(x - 24) = 0
⇒ (x + 4)(x – 24) = 0
⇒ x + 4 = 0 or x - 24 = 0
⇒ x = -4 or x = 24 cm
Since, side of a square cannot be negative.
∴ x ≠ -4.
Side of square = 24 cm
Perimeter of square = 4 × side = 4 × 24
= 96 cm.
Hence, perimeter of square = 96 cm.
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