The perimeters of two squares are 60 metres and 144 metres respectively. Find the perimeters of another square equal in area to the sum of the first to squares.

We know, Perimeter of square = 4 × side

Area of square = (side)²

Let the side of two squares be a₁ and a_2. Side of third square be ‘a’

Given,

Perimeter of first square = 60

⇒ 4a₁ = 60

⇒ a₁ = 15

⇒ a₁² = 225

Area of first square = 225 m²

Perimeter of second square = 144

⇒ 4a₂ = 144

⇒ a₂ = 36

⇒ a₂² = 1296

Area of second square = 1296 m²

Also,

Area of third square = 225 + 1296

⇒ a² = 1521

⇒ a = 39

⇒ 4a = 156 m

Hence, perimeter of third square is 156 m.