If the sides of a square are lengthened by 3 cm, the area becomes 121 cm 3 . Find the perimeter of the original square.

Mathematics

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Let length of square be x cm.

New length = (x + 3) cm.

According to the question,

⇒ (x + 3)(x + 3) = 121

⇒ x² + 3x + 3x + 9 = 121

⇒ x² + 6x = 112

⇒ x² + 6x - 112 = 0

⇒ x² + 14x - 8x - 112 = 0

⇒ x(x + 14) - 8(x + 14) = 0

⇒ (x - 8)(x + 14) = 0

⇒ x - 8 = 0 or x + 14 = 0

⇒ x = 8 or x = -14.

Since, length cannot be negative.

∴ x ≠ -14.

Perimeter of original square = 4 × side = 4x

= 4 × 8 = 32 cm.

Hence, perimeter of original square = 32 cm.

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