Question

If the sides of a triangular field measure 51 m, 37 m and 20 m, then the cost of levelling it at Rs 5 per m² is Rs 1530.

Answer 1

True

$$\begin{gathered} \mathrm{Let}: \\ a=51\mathrm{m},b=37\mathrm{m}\mathrm{and}c=20\mathrm{m} \\ s=\frac{a+b+c}{2}=\frac{51+37+20}{2}=54\mathrm{m} \\ \mathrm{By}\mathrm{Heron}\text{'}\mathrm{s}\mathrm{formula},\mathrm{we}\mathrm{have}: \\ \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{54(54-51)(54-37)(54-20)} \\ =\sqrt{54\times 3\times 17\times 34} \\ =\sqrt{3\times 3\times 3\times 2\times 3\times 17\times 17\times 2} \\ =17\times 2\times 3\times 3 \\ =306{\mathrm{m}}^2 \end{gathered}$$
Cost of levelling 1 m² of area = Rs 5
Cost of levelling 306 m² of area = $5\times 306=\mathrm{Rs}1530$