Question

The base of a triangular field is three times its height. If the cost of cultivating the field is $Rs1080$ per hectare. If the total cost of cultivating the field is $Rs14580$. find its base and height.

Answer 1

Given

Let ABC be a triangle and CD is $\perp$ to AB.

Given AB = 3CD---(1)

cost of cultivating per hectare = 1080

Total cost in cultivating field ABC = 14580 Rs

So area of field ABC $=\frac{14580}{1080}$ hectare

area of field ABC $=13.5$ hectare

or $135000m^2$

Now we know

area of triangle $=\frac{1}{2}(AB\times CD)$

using eq(1) we get

$\frac{1}{2}\times 3CD\times CD=135000$

$(CD{)}^2=\frac{270000}{3}=90000$

$CD=300m$

and $AB=900m$

Hence height of field is $=300m$

and Base of field is $=900m$