Question

If the diagonal of a square is `12 sqrt 2` cm then the perimeter of square is ______.

Options

• 24 cm

• `24sqrt2` cm

• 48 cm

• `48 sqrt2` cm

Answer 1

If the diagonal of a square is `12 sqrt 2` cm then the perimeter of square is 48 cm.

Explanation:

Let the diagonal be AC = `12 sqrt 2`

Since it is a square so, all the angles are 90°.

In ΔABC, we apply the Pythagoras theorem,

AB² + BC² = AC²

⇒ AB² + AB² = AC²     (∵ `square`ABCD is a square.)

⇒ 2 AB² = AC²

⇒ 2 AB² = `(12 sqrt 2)^2`

⇒ 2 AB² = 288

⇒ AB² = 144

⇒ AB = 12 cm

∴ AB = BC = CD = AD = 12 cm

Perimeter of `square`ABCD = 4AB

= 4 × 12 cm

= 48 cm