The sides of a triangular field are 975 m, 1050 m and 1125 m. If this field is sold at the rate of ₹ 10 lakh per hectare, find its selling price. [1 hectare = 10000 m²]

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,

$s = \dfrac{(975 + 1050 + 1125)}{2}\\[1em] = \dfrac{3150}{2}\\[1em] = 1575 \text{ m}.$

By formula,

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

Substituting values we get :

$A = \sqrt{1575(1575 - 975)(1575 - 1050)(1575 - 1125)}\\[1em] = \sqrt{1575 \times 600 \times 525 \times 450}\\[1em] = \sqrt{(525 \times 3) \times (150 \times 2 \times 2) \times (525) \times (150 \times 3)}\\[1em] = \sqrt{525^2 \times 150^2 \times 2^2 \times 3^2}\\[1em] = 525 \times 150 \times 2 \times 3\\[1em] = 472500 \text{ m}^2 \\[1em] = \dfrac{472500}{10000} \\[1em] = 47.25 \text{ hectares}.$

We know that,

Selling price of 1 hectare field = ₹ 10 lakh.

∴ Selling price of 47.25 hectare field = ₹ 10,00,000 × 47.25 = ₹ 4,72,50,000.

Hence, selling price of the triangular field = ₹ 4,72,50,000.