The diagonal of a square is 15 m; find the length of its one side and perimeter.

Given:

Diagonal of the square is 15 m.

Let each side of the square be a m.

Then, by using Pythagoras theorem,

⇒ Diagonal² = Side² + Side²

⇒ (15)² = a² + a²

⇒ 225 = 2a²

⇒ a² = $\dfrac{225}{2}$

⇒ a² = 112.5

⇒ a = $\sqrt{112.5}$

⇒ a = 10.6

As we know that perimeter of the square = 4 x side

= 4 x 10.6 m

= 42.4 m

Hence, the side of square is 10.6 m and its perimeter is 42.4 m.