Question

The area of a rectangle of length 6 cm and breadth 24 cm is equal to the area of a square. What will be the length of the diagonal of the square?

1. 14√7 cm
2. 12√5 cm
3. 12√2 cm
4. 7√12 cm

Answer 1

Correct Answer - Option 3 : 12√2 cm

Given:

Length of rectangle = 6 cm

Breadth of the rectangle = 24 cm

Area of rectangle = Area of square

Concept:

Area of rectangle = (l × b) cm²

Area of square = (a × a) cm²

Diagonal of square = √2 a cm

Calculation:

Area of rectangle = (6 × 24) cm² = 144 cm²

Area of square = 144 cm²

∴ Side of the square = √144 = 12 cm

∴ Diagonal of the square = √2 × 12 = 12√2 cm