Question

The diagonal of square is 5√2 unit, and perimeter of rectangle is twice the perimeter of square. If breadth is 2 unit less than length of the rectangle. Find area of rectangle (In unit²)
1. 100
2. 121
3. 99
4. 90

Answer 1

Correct Answer - Option 3 : 99

Given:

Diagonal of square = 5√2 unit

Length – breadth = 2 unit

Perimeter of rectangle = 2 × perimeter of square

Formula used:

Diagonal of square = a√2, where a = side of the square

Perimeter of square = 4a

Perimeter of rectangle = 2 (l + b), where l = length and b = breadth of rectangle

Area of rectangle = l × b = lb

Diagonal of square = a√2

Calculation:

∴ a√2 = 5√2

∴ a = 5 unit

⇒ Perimeter of square = 4a = 4 × 5 = 20 unit

⇒ Perimeter of rectangle = 2 (l + b), where (l = length and b = breadth)

∴ 2 (l + b) = 20 × 2 = 40

∴ (l + b) = 20     ---- (1)

⇒ l – b = 2     ---- (2)

On equating eqn. (1) and (2)

l = 11 and b = 9

Therefore, area of rectangle = 11 × 9 = 99 unit²