Question

Choose the correct answer of the following question:

The lengths of the sides of a triangular field are 20 m, 21 m and 29 m. The cost of cultivating the field at ₹9 per m² is

(a) ₹2610 (b) ₹3780 (c) ₹1890 (d) ₹1800

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{are}20\mathrm{m},21\mathrm{m}\mathrm{and}29\mathrm{m} \\ \mathrm{So},\mathrm{the}\mathrm{semi}-\mathrm{perimeter}=\frac{20+21+29}{2}=35\mathrm{m} \\ \mathrm{Now},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{triangular}\mathrm{field}=\sqrt{35\left(35-20\right)\left(35-21\right)\left(35-29\right)} \\ =\sqrt{35\times 15\times 14\times 6} \\ =\sqrt{7\times 5\times 5\times 3\times 7\times 2\times 2\times 3} \\ =2\times 3\times 5\times 7 \\ =210{\mathrm{m}}^2 \\ \therefore \mathrm{The}\mathrm{cost}\mathrm{of}\mathrm{cultivating}\mathrm{the}\mathrm{field}=210\times 9=₹1890 \end{gathered}$$

Hence, the correct answer is option (c).