Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Find the height corresponding to the longest side.

Let $a,b$ and $c$ be the sides of a triangle.
Apply Heron's Formula to find the area of triangle.
Area $=\sqrt{S(S-a)(S-b)(S-c)}$
Whee $S=\frac{a+b+c}{2}$
Here $a=42cm,b=34cm$ and $c=20cm$
$S=\frac{(42+34+20)}{2}=48$
Area $=\sqrt{(48(48-42)(48-34)(48-20))}$
         $=\sqrt{(48\times 6\times 14\times 28)}$
         $=336$
Area of triangle is $336c{m}^2$

Clearly,
Length of longest side $=42cm$
Also we know,
Area of a triangle $=\frac{1}{2}\times Base\times Height$
$\Rightarrow 336=\frac{1}{2}\times 42\times Height$
$\Rightarrow 336=21\times Height$
or Height $=16$
The height corresponding to the longest side is $16cm$