Mathematics

Find the area and perimeter of a square plot of land, the length of whose diagonal is 15 metres. Give your answer correct to 2 places of decimals.

20 Likes

Given:

Diagonal of the square = 15 m

Let a be the length of side of the square.

Using the Pythagoras theorem for a square,

⇒ Side² + Side² = Diagonal²

⇒ 2 x Side² = Diagonal²

⇒ 2 x a² = 15²

⇒ 2a² = 225

⇒ a² = $\dfrac{225}{2}$

⇒ a² = 112.5

⇒ a = $\sqrt{112.5}$

⇒ a = 10.61 m

Area of square = side²

= 10.61² m²

= 112.5 m²

Perimeter of square = 4 x side

= 4 x 10.60 m

= 42.43 m

Hence, the area of the square plot is 112.5 m² and the perimeter is 42.43 m.

Answered By

14 Likes