The sides of a triangular field are 975 m, 1050 m and 1125 m. If this field is sold at the rate of ₹ 1000 per hectare, find its selling price.

Consider a = 975 m, b = 1050 m and c = 1125 m.

We know that,

Semi perimeter (s) = $\dfrac{(a + b + c)}{2}$

Substituting the values we get,

s = $\dfrac{(975 + 1050 + 1125)}{2} = \dfrac{3150}{2}$ = 1575 m.

Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

Substituting values we get,

$A = \sqrt{1575(1575 - 975)(1575 - 1050)(1575 - 1125)} \\[1em] = \sqrt{1575 \times 600 \times 525 \times 450} \\[1em] = \sqrt{(525 \times 3) \times (150 \times 2 \times 2) \times (525) \times (150 \times 3)} \\[1em] = \sqrt{(525)^2 \times (150)^2 \times (2)^2 \times (3)^2} \\[1em] = 525 \times 150 \times 2 \times 3 \\[1em] = 472500 \text{ m}^2.$

Given,

1 hectare = 10000 m².

So,

472500 m² = $\dfrac{472500}{10000}$ = 47.25 hectares.

We know that,

Selling price of 1 hectare field = ₹ 1000.

∴ Selling price of 47.25 hectare field = ₹ 1000 × 47.25 = ₹ 47250.

Hence, selling price of the triangular field = ₹ 47250.