Question

The length of a rectangular field exceeds its breadth by 8 m and the area of the field is 240 m². The breadth of the field is ______.

Options

• 20 m

• 30 m

• 12 m

• 16 m

Answer 1

The length of a rectangular field exceeds its breadth by 8 m and the area of the field is 240 m². The breadth of the field is 12 m.

Explanation:

Let the breadth of the rectangular field be x m.

∴ Length of the rectangular field = (x + 8) m 

Area of the rectangular field = 240 m²    ...(Given) 

∴ (x + 8) × x = 240   ...(Area = Length × Breadth)

⇒ x² + 8x – 240 = 0 

⇒ x² + 20x – 12x – 240 = 0 

⇒ x(x + 20) – 12(x + 20) = 0 

⇒ (x + 20)(x – 12) = 0 

⇒ x + 20 = 0 or x – 12 = 0 

⇒ x = –20 or x = 12 

∴ x = 12   ...(Breadth cannot be negative) 

Thus, the breadth of the field is 12 m.

Hence, the correct answer is option C.