The sides of a square are all increased by 3 cm. The area of the new square is 64 cm'.

Find the length of a side of the original square.

Side of the original square is 5 cm.

Step-by-step explanation:

Step 1: Let the side of the original square be x. Then side of the new square = x + 3 and Area of new square = 64 cm²

Area of a square = (side) ²

⇒ 64 = (x + 3) ²

⇒ 64 = x² + 6x + 9

⇒ x² + 6x - 55 = 0

⇒ x² + 11x - 5x - 55 = 0 (Since 6x = 11x - 5x as part of factorizing)

⇒ x (x + 11) - 5 (x + 11) = 0

⇒ (x + 11) (x - 5) = 0

⇒ x = - 11 and x = 5 (Lengths can't be negative)

Side of the original square is 5 cm.