The perimeter of two squares are 20 cm and 24 cm.  Find the perimeter of third square whose area is equal to the sum of area of these two squares.

4\(\sqrt {61}\) cm

Square I

⇒ side (s₁) = \(\frac{perimeter}{4}\) = \(\frac{20}{4}\) = 5 cm

Square II

⇒ side (s₂) = \(\frac{perimeter}{4}\) = \(\frac{24}{4}\) = 6 cm

Area of square III = (s₁)² + (s₂)² = 5² + 6² = 61 cm^₂

Side of square III = \(\sqrt {61}\) cm

Perimeter of 3rd square = 4\(\sqrt {61}\) cm