Question

The base of a triangular field is three times its altitude. If the cost of sowing the field at $Rs.58$ per hectare is $Rs.783,$ find its base and height.

Answer 1

Let the altitude of the triangle be $y$
Then the base will be $3y$

Area of triangle $=\frac{1}{2}\times$ base$\times$ altitude
$=\frac{1}{2}\times 3y\times y$
$=\frac{1}{2}\times 3y^2$
$=\frac{3y^2}{2}$

Cost of sowing in $1$ hactare of land $=Rs.58$

so, the cost of sowing in $10000m^2$ land $=Rs58$ [$\because 1$ hactare $=10000m^2$]

then, the cost of sowing in $1m^2$ land $=Rs\frac{58}{10000}$

Total Cost of sowing the field $\frac{3y^2}{2}$ of land $=\frac{58}{10000}\times \frac{3y^2}{2}=\frac{87y^2}{10000}$

Therefore, $\frac{87y^2}{10000}=783$ [$\because$ Total area of sowing is given as $Rs.783$]

$\Rightarrow y^2=\frac{783\times 10000}{87}=90000$

$\Rightarrow y=300$

Base $=3\left(3\right)=900m$

Hence base is $900m$ and altitude is $300m.$