Question

When each side of a square was reduced by 3 meter, the area became 81 square
meter
What was the length of the sides of the orginal squre?​

Answer 1

⌬ Let side of square be x cm.

According to the given Question:

Each side of a square was reduced by 3 meter, the area became 81 m².

Sides of square after reducing 3 m,

• Sides = (x - 3) m

We know that,

Area of square = side × side

⇏ (x - 3)(x - 3) = 81

⇏ x² - 3x - 3x + 9 = 81

⇏ x² - 6x + 9 = 81

⇏x² - 6x + 9 - 81 = 0

⇏ x² - 6x - 72 = 0

⇏ x² - 12x + 6x - 72 = 0

⇏x(x - 12) 6(x - 12) = 0

⇏ (x - 12)(x + 6) = 0

⇏x = 12, - 6

Since, Side of a square can't be negative.

⇏x = 12 m

Hence, original side of the square is 12 m.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Verification:

• Side of square after reducing 3 m

⇏ 12 - 3 = 9 m

Area of square after reducing 3 m from side,

⇏9 × 9 = 81 m²

Hence, Verified!!