Question

The sides of a triangular field are 975 m, 1050 m and 1125 m. If this field is sold at the rate of ₹ 100 per hectare, find its selling price. [Note : 1 hectare = 10000 m²]

Answer 1

Given: The sides of the triangular field are 975 m, 1050 m and 1125 m. The selling rate is ₹ 100 per hectare (1 hectare = 10000 m²).

Step-wise calculation:

1. Let a = 975 m, b = 1050 m, c = 1125 m.

2. Semi-perimeter `s = (a + b + c)/2`

= `(975 + 1050 + 1125)/2`

= `3150/2`

= 1575 m

3. s – a

= 1575 – 975

= 600

s – b

= 1575 – 1050

= 525

s – c

= 1575 – 1125

= 450

4. Area (Heron’s formula) = `sqrt(s(s - a)(s - b)(s - c))`

= `sqrt((1575 × 600 × 525 × 450))` 

Noting 975 : 1050 : 1125 = 75 × (13 : 14 : 15), the triangle is a 13 – 14 – 15 scaled by 75.

Area of 13 – 14 – 15 triangle = 84. 

So, area = 84 × 75²

= 84 × 5625

= 4,72,500 m²

5. Convert to hectares:

4,72,500 m² ÷ 10,000

= 47.25 hectares

6. Selling price

= 47.25 hectares × ₹ 100/hectare 

= ₹ 4,725

The selling price of the field is ₹ 4,725.