Question

The perimeter of a triangular field is 540 m, and its sides are in the ratio 25:17:12. Find the area of the field. Also, find the cost of ploughing the field at ₹40 per 100 m².

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{triangular}\mathrm{field}\mathrm{be}25x,17x\mathrm{and}12x. \\ \mathrm{As},\mathrm{perimeter}=540\mathrm{m} \\ \Rightarrow 25x+17x+12x=540 \\ \Rightarrow 54x=540 \\ \Rightarrow x=\frac{540}{54} \\ \Rightarrow \mathrm{x}=10 \\ \mathrm{So},\mathrm{the}\mathrm{sides}\mathrm{are}250\mathrm{m},170\mathrm{m}\mathrm{and}120\mathrm{m}. \\ \mathrm{Now},\mathrm{semi}-\mathrm{perimeter},s=\frac{250+170+120}{2}=\frac{540}{2}=270\mathrm{m} \\ \mathrm{So},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{field}=\sqrt{270\left(270-250\right)\left(270-170\right)\left(270-120\right)} \\ =\sqrt{270\times 20\times 100\times 150} \\ =\sqrt{3^3\times 10\times 2\times 10\times {10}^2\times 3\times 5\times 10} \\ =3^2\times {10}^3 \\ =9000{\mathrm{m}}^2 \\ \mathrm{Also},\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{ploughing}\mathrm{the}\mathrm{field}=\frac{9000\times 40}{100}=₹3,600 \end{gathered}$$