Question

The perimeters of two squares are 40 and 96 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Answer 1

Given: Perimeter of one square = 40 m

Let length of square = a₁

Then 4a₁ = 40 m

⇒ a₁ = 10 m

Area of square = a₁ × a₁

= 10 × 10

= 100 m²

Perimeter of second square = 96 m

Let length of square = a₂

Then 4a₂ = 96 m

⇒ a₂ = 24 m

Area of square = a₂ × a₂

= 24 × 24

= 576 m²

Because, perimeter of another square equal in area to the sum of the first two squares.

Hence, area of another square = 100 + 576 = 676 m

Area of square = a₃ × a₃

676 = (a₃)²

⇒ a₃ = 26 m

Hence, perimeter = 4a₃

= 4 × 26

= 104 m