Question

Find the area of the triangle as well as as the height to the longest side of the triangle whose sides are:
$9cm,10cm$ and $17cm$

Answer 1

$S=\frac{9+10+7}{2}=18$ Area = $\sqrt{S(S-a)(S-b)(S-c)}$

Area = $\sqrt{18\times 1\times 8\times 9}=36c{m}^2$

Height corresponding to $17$ cm be h

Area $=\frac{1}{2}\times 17\times h$

$\Rightarrow h=\frac{36\times 2}{17}=4.23$cm.