Find the perimeter of a square whose area is equal to half the sum of areas of three squares with sides 3 cm, 4 cm and 5 cm.

Given:

Area of square = Half the sum of areas of three squares with sides 3 cm, 4 cm and 5 cm.

Let R be the side of the square.

As we know that area of the square = side²

$⇒ R^2 = \dfrac{1}{2} \times (3^2 + 4^2 + 5^2)\\[1em] ⇒ R^2 = \dfrac{1}{2} \times (9 + 16 + 25)\\[1em] ⇒ R^2 = \dfrac{1}{2} \times 50\\[1em] ⇒ R^2 = 25\\[1em] ⇒ R = \sqrt{25}\\[1em] ⇒ R = 5 \text{ cm}$

And, perimeter of the square = 4 x side

Perimeter of the square = 4 x 5 cm

= 20 cm

Hence, the perimeter of the square is 20 cm.