Question

The lengths of the sides of a triangular field measure 20 m, 21 m and 29 m. The cost of cultivating the field at Rs 4.50 per m² is
(a) Rs 900
(b) Rs 945
(c) Rs 1305
(d) Rs 1890

Answer 1

(b) Rs 945

We will find the semiperimeter, s, of the field.

$$\begin{gathered} s=\frac{1}{2}\left(a+b+c\right) \\ =\frac{1}{2}\left(20+21+29\right) \\ =\frac{1}{2}\left(70\right) \\ =35\mathrm{m} \end{gathered}$$

Now,
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{35(35-20)(35-21)(35-29)} \\ =\sqrt{35\times 15\times 14\times 6} \\ =\sqrt{44100} \\ =210{\mathrm{m}}^2 \end{gathered}$$

∴ Total cost of cultivating 210 m² of the field at the rate of Rs 4.50 per metre = $4.50\times 210=\mathrm{Rs}945$