Question

The diagonal of a rectangular field is 18 m and its area is 126 m². What will be the total expenditure in fencing the field at the rate of Rs. 9 per metre?
1. Rs. 432
2. Rs. 420
3. Rs. 442
4. Rs. 430

Answer 1

Correct Answer - Option 1 : Rs. 432

Given:

Diagonal of a rectangular field = 18 m

Area = 126 m2 

Rate of fencing = Rs 9/m

Concept used:

Area of the rectangular field = l × b

l - length , b - breadth

Diagonal of the rectangle field = √(l² + b²)

Perimeter = 2 × (l + b)

Calculation:

√(l2 + b2) = 18

Or, (l2 + b2) = 18²      ----(1)

l × b = 126      ----(2)

(1) + 2 × (2), we get,

(l2 + b2) + 2 lb = 18² + 2 × 126

(l + b)² = 324 +  252 = 576

(l + b) = √576 = 24

Perimeter = 2 × (l + b) = 2 × 24 = 48 m

Total cost of fencing the field = 9 × 48 = Rs 432.

∴ The total cost of fencing is Rs 432.