The perimeters of two squares are 52 cm and 20 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of these two squares.

Given:

The perimeters of two squares are 52 cm and 20 cm.

Concept used:

Perimeter of square = 4 × side

Area = Side²

Calculation:

Side of first square = \(\dfrac{52}{4}\) = 13 cm

Side of second square = \(\dfrac{20}{4}\) = 5 cm

Area of first square = 13 × 13 = 169 cm²

Are of second square = 5 × 5 = 25 cm²

Difference in area = Area of third square = 169 - 25 = 144 cm²

Side of third square = √144 = 12 cm

Perimeter of third square = 4 × 12 = 48 cm.

∴ The perimeter of the third square is 48 cm.