Question

A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3 and its area is 3375 m². Find the cost of fencing the lawn at ₹ 20 per metre.

Answer 1

Given: A rectangular lawn with sides in the ratio 5 : 3 and area 3375 m². Cost of fencing = ₹ 20 per metre.

Step-wise calculation:

1. Let the sides be 5x and 3x.

Area = (5x)(3x)

= 15x²

2. 15x² = 3375

⇒ x² = 3375 ÷ 15

⇒ x² = 225

⇒ x = `sqrt(225)`

⇒ x = 15 m

3. Dimensions:

Length = 5x 

= 5 × 15

= 75 m

Breadth = 3x

= 3 × 15

= 45 m

4. Perimeter = 2(Length + Breadth)

= 2(75 + 45)

= 2 × 120

= 240 m

5. Cost of fencing = Perimeter × Rate

= 240 × ₹ 20

= ₹ 4800

The cost of fencing the lawn is ₹ 4,800.