Question

The base of a triangular field is `2 1/2` times its height. If the cost of turfing it at ₹ 48 per 100 sq. m is ₹ 960, find its base.

Answer 1

Given: The base (b) of a triangular field is `2 1/2` times its height (h). 

Turfing rate = ₹ 48 per 100 sq. m; total cost = ₹ 960.

Step-wise calculation:

1. Find area from cost:

Area = `"Total cost"/"Rate" xx 100` 

= `960/48 xx 100` 

= 20 × 100

= 2000 sq. m.

2. Relate area to base and height:

`b =  5/2 h`   ...`("Since"  2 1/2 = 5/2)`

Area of triangle = `1/2 xx b xx h`

= 2000

Substitute b:

`1/2 xx 5/2 h xx h = 2000` 

⇒ `5/4 h^2 = 2000`

⇒ `h^2 = 2000 xx 4/5`

⇒ h² = 1600

⇒ `h = sqrt(1600)`

⇒ h = 40 m

3. Find base:

`b = 5/2 xx 40` 

= 2.5 × 40

= 100 m

Base of the triangular field = 100 metres.