Question

The perimeters of four squares are 32 cm, 36 cm, 40 cm, and 56 cm respectively. The perimeter of another square that has an area equal to the sum of areas of these four squares is.
1. 84 cm
2. 80 cm
3. 86 cm
4. 82 cm

Answer 1

Correct Answer - Option 1 : 84 cm

GIVEN:
Perimeter = 32 cm, 36 cm, 40 cm, 56 cm

FORMULA USED:

Perimeter of square = 4 × side

Area of square = side²

CALCULATION:

Sides of squares = 32/4, 36/4, 40/4, 56/4

⇒ 8 cm, 9 cm, 10 cm, 14 cm

Sum of areas of squares = 8² + 9² + 10² + 14²

⇒ 64 + 81 + 100 + 196 = 441 cm²

Area of large square = 441 cm²

Side = √441 = 21 cm

Perimeter = 4 × 21 = 84 cm

∴ Perimeter is 84 cm.