In the adjoining figure, A, B and C are squares. If the area of the square A is 25 sq. cm and the perimeter of the square B is 12 cm, then find the perimeter and the area of the square C.

Given:

Area of square A = 25 sq. cm

Perimeter of square B = 12 cm

For square A:

Area of square = side × side

⇒ 25 = side × side

⇒ side² = 25

⇒ side = $\sqrt{25}$

⇒ side of A = 5 cm

For square B:

Perimeter of square = 4 × side

⇒ 12 = 4 × side

⇒ side = $\dfrac{12}{4}$

⇒ side of B = 3 cm

From the figure, side of square C = side of A + side of B

= 5 + 3

= 8 cm

Perimeter of square C = 4 × side

= 4 × 8

= 32 cm

Area of square C = side × side

= 8 × 8

= 64 sq. cm

Hence, the perimeter of square C is 32 cm and the area is 64 sq. cm.