Question

The sides of a triangle are $16cm,12cm$ and $20cm$. Find the height of the triangle in $mm$, corresponding to the largest side.

Answer 1

Area of triangle with $a,b,c$ as sides and
$s=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides $16cm,12cm$ and $20cm$, $s=\frac{16+12+20}{2}=24cm$
Area of the triangle with sides $16cm,12cm$ and $20cm$ $=\sqrt{24(24-16)(24-12)(24-20)}$

$=\sqrt{24\times 8\times 12\times 4}$

$=\sqrt{8\times 3\times 8\times 4\times 3\times 4}$

$=8\times 3\times 4$

$=96{cm}^2$

Area of triangle can also be calculated using the formula $\frac{1}{2}\times \text{base}\times \text{height}$

Let the height for base $20cm$, be.
So, area $=\frac{1}{2}\times 20\times h=96{cm}^2$

$\Rightarrow h=9.6cm=96mm$