Question

The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. $24.68$ per hectare be Rs. $333.18$, find its base and height

Answer 1

Area of the field$=\frac{Totalcost}{rate}$

$=\frac{333.18}{25.6}=13.5$hectares

Let altitude$=x$metres and base$=3x$metres

Then $\frac{1}{2}\times 3x\times x=135000$

$\Rightarrow x^2=\frac{135000\times 2}{3}$

$\Rightarrow x^2=45000\times 2=90000$

$\Rightarrow x=\sqrt{90000}=300$m

Base$=900$m and altitude$=300$m