Question

The ratio of the length to the perimeter of a rectangular board is 3 : 10. Then, find the area of the board, if the breadth of the board is 8 m.
1. 84 m²
2. 96 m²
3. 90 m²
4. 108 m²

Answer 1

Correct Answer - Option 2 : 96 m²

Given:

The ratio of length to the perimeter of board = 3 : 10

Breadth of board = 8 m

Formula Used:

Perimeter of rectangle = 2 × (Length + Breadth)

Area of rectangle = Length × Breadth

Calculation:

Let the length of board be '3x' and perimeter be '10x'

Now, Perimeter of rectangle = 2 × (3x + 8)

⇒ 10x = 6x + 16

⇒ 4x = 16

⇒ x = 16/4 = 4 m

So, length of board = 3x = 12 m

Now, area of board = length × breadth 

⇒ 12 × 8 = 96 m²

∴ The area of board is 96 m².