Question

What is the ratio of area of rectangle whose length and breadth is 12 cm and 8 cm to area of square defined by the diagonal of rectangle?
1. 6 ∶ 13
2. 13 ∶ 6
3. 11 ∶ 10
4. 10 ∶ 11

Answer 1

Correct Answer - Option 1 : 6 ∶ 13

Given:

The length and breadth of rectangle is 12 cm and 8 cm

Formula used:

Area of rectangle = Length × breadth

Length of diagonal of rectangle = √l² + b²

Area of square = side × side

Calculation:

Area of rectangle = 12 × 8 = 96 square cm

Now, diagonal of rectangle = √l² + b² = √(12)² + (8)² = 4√13 cm

∴ Area of square defined from the diagonal of rectangle = 4√13 × 4√13 = 208 square cm

Now, ratio of area of rectangle to area of square defined by the diagonal of rectangle = 96 ∶ 208 = 6 ∶ 13

Hence, option (1) is correct