# The base of a triangular field is three times its altitude.

Question:

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.

Solution:

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