Question

The altitude of a triangular field is one-third of its base. If the cost of sowing the field at Rs.58 per hectare is Rs.783 then find its altutude

Answer 1

Let the base of the triangle be x

Hence altitude =$\frac{x}{3}$

Area of triangle = $\frac{1}{2}$ × base × height

=$\left(\frac{1}{2}\right)\times \left(x\right)\times \left(\frac{x}{3}\right)=\frac{x^2}{6}$

Cost of sowing the field at rs 58 per hectare $=58\times \frac{x^2}{6}$
$=\frac{29x^2}{3}$

Therefore, $\frac{29x^2}{3}{m}^2=783hectare$

$\Rightarrow \frac{29x^2}{3}{m}^2=783\times {10}^4{m}^2$

$x^2=\frac{783\times 3\times {10}^4}{29}=8100$

⇒ x = 9

so altitude =$\frac{9}{3}=3$

Hence, base is 9 and altitude is 3.