Question

The sides of a triangular field are 975 m, 1050 m and 1125 m. If this field is to be sold at the rate Rs 1000 per hectare (1 hectare =10000 m²), find its selling price.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{triangle}\mathrm{be}\mathrm{a}=975\mathrm{m},\mathrm{b}=1050\mathrm{m},\mathrm{c}=1125\mathrm{m} \\ \mathrm{Now},\mathrm{s}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}=\frac{975+1050+1125}{2}=1575\mathrm{m} \\ \mathrm{Area}\mathrm{of}\mathrm{trianglular}\mathrm{field}=\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)} \\ =\sqrt{1575\left(1575-975\right)\left(1575-1050\right)\left(1575-1125\right)} \\ =\sqrt{1575\times 600\times 525\times 2700} \\ =\sqrt{3^2\times 5^2\times 7\times 2^3\times 3\times 5^3\times 3\times 5^2\times 7\times 2^2\times 3^3\times 5^2} \\ =\sqrt{3^7\times 5^9\times 7^2\times 2^5} \\ =3^3\times 5^4\times 7\times 2^2\sqrt{3\times 5\times 2} \\ =472500\sqrt{30}{\mathrm{m}}^2 \\ =\frac{472500\sqrt{30}}{10000}\mathrm{hectare} \\ =47.25\sqrt{30}\mathrm{hectare} \\ \mathrm{Selling}\mathrm{price}=\mathrm{Rs}1000\times 47.25\sqrt{30}=\mathrm{Rs}47250\sqrt{30} \end{gathered}$$
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