Question

Two squares have sides x cm and (2x + 1) cm, respectively. The sum of their perimeters is 100 cm. Area (in cm²) of the bigger square is
1. 64
2. 81
3. 225
4. 289

Answer 1

Correct Answer - Option 4 : 289

Given:

Side of first square = x cm

Side of second square = (2x + 1) cm

Sum of their perimeter = 100 cm

Formula used:

Perimeter = 4 × Side of square

Area = (Side of square)²

Calculations:

Perimeter of first square = 4x

Perimeter of second square = 4 × (2x + 1) 

⇒ 8x + 4

Sum of their perimeters = 4x + (8x + 4)

⇒ 12x + 4 = 100

⇒ 12x = 96

⇒ x = 8

Side of first square = 8 cm

Side of second square = (2 × 8 + 1) = 17 cm

Area of the bigger square = 17 × 17

⇒ 289 cm²

∴ The area of the bigger square is 289 cm²