Question

The base of a triangular field is three times its height and its area is $1350m^2.$ Find the base and height of the field.

Answer 1

Let the base of the triangular field be $3xm$ and its height be $xm.$

Then, area of the triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times 3x\times x{m}^2$
$=\frac{3x^2}{2}{m}^2$
But it is given that the area of the triangular field is $1350m^2.$
$\frac{3x^2}{2}=1350$

$\Rightarrow 3x^2=1350\times 2$

$\Rightarrow x^2=900$

$\Rightarrow x=\sqrt{900}$

$\Rightarrow x=30m$
Hence, the height of the field is $30m.$

Its base $=3\times 30m=90m$