Question

The base of a triangular field is three times its altitude. If the cost of sowing seeds in the field at 58/- per hectare is 783/-,find base and altitude.

Answer 1

Let the altitude of the triangle be x
Hence base = 3x
Area of triangle = (1/2) × base × height
=$\frac{1}{2}$ × (x) × (3x) = $\frac{3x^2}{2}{m}^2$
Cost of sowing the field at rs 58 per hectare =$58\times \frac{3x^2}{2}\times {10}^4$
As 1 hectare =${10}^4{m}^2$
= $87x^2\times {10}^4$
Therefore, $87\times x^2\times {10}^4=783$
x² =$\frac{783}{87}=90000$
⇒ x = 300 m
Base = 3(300) = 900 m
Hence base is 900 m and altitude is 300 m.