Question

 Length of rectangle is 7cm more than its breadth. Length of the diagonal of the rectangle is 13cm. What is the area of the square having perimeter same as perimeter of given rectangle ?
1. 56.25 cm²
2. 55 cm²
3. 72.25 cm²
4. 32.25 cm²

Answer 1

Correct Answer - Option 3 : 72.25 cm²

Given:

Length of rectangle is 7cm more than its breadth. Length of the diagonal of the rectangle is 13cm

Concept used:

Mensuration

Calculation:

Diagonal of the rectangle is 13 cm 

Let the breadth of the rectangle be x cm

Length = x + 7 cm

⇒ L² + B² = D²

⇒ (x + 7)² + x² = 13²

⇒ 2x² + 14x + 49 = 169

⇒ 2x² + 14x - 120 = 0

⇒ x² + 7x - 60 = 0

⇒ (x + 12) (x - 5) = 0

∴ x = 5 cm

which gives Length = 5 + 7 = 12 cm and Breadth = 5 cm.

Perimeter of rectangle = 2 (L + B)

Perimeter of rectangle = 2 (12 + 5)

Perimeter = 34 cm.

As per the question, Perimeter of rectangle = Perimeter of Square

Perimeter of square = 34 cm

4 × side of square = Perimeter of square

side of square = 34/4 = 8.5 cm

Area of square = a²

Area of square =  8.5² = 72.25 cm²