The base of a triangular field is three times its altitude. If the cost of sowing the field at Rs 58 per hectare is Rs 783, find its base and height.
Let the height of the triangle be h m.
∴ Base = 3h m
Now,
Area of the triangle $=\frac{\text { Total Cost }}{\text { Rate }}=\frac{783}{58}=13.5 \mathrm{ha}=135000 \mathrm{~m}^{2}$
We have:
Area of triangle $=135000 \mathrm{~m}^{2}$
$\Rightarrow \frac{1}{2} \times$ Base $\times$ Heigh $t=135000$
$\Rightarrow \frac{1}{2} \times 3 h \times h=135000$
$\Rightarrow h^{2}=\frac{135000 \times 2}{3}$
$\Rightarrow h^{2}=90000$
$\Rightarrow h=300 \mathrm{~m}$
Thus, we have:
Height = h = 300 m
Base = 3h = 900 m
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