Question

The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs 24.60 per hectare is Rs 332. 10, find its base and height.

Answer 1

Let altitude of the triangular field be h m
Then base of the triangular field is 3h m.

Area of the triangular field = $\frac{1}{2}\times h\times 3h=\frac{3h^2}{2}{\mathrm{m}}^2$..........(i)

The rate of cultivating the field is Rs 24.60 per hectare.
Therefore,
Area of the triangular field = $\frac{332.10}{24.60}=13.5\mathrm{hectare}$
= 135000 m² [Since 1 hectare = 10000 m² ]..........(ii)
From equation (i) and (ii) we have,
$\frac{3h^2}{2}=135000{\mathrm{m}}^2$
3h² = 135000 x 2 = 270000 m²

h² = $\frac{270000}{3}\mathrm{m}$²=90000 m2 = (300 m)²
⇒ h = 300 m

Hence,
Height of the triangular field = 300 m and base of the triangular field = 3 x 300 m = 900 m