Question

Find the area of a triangle whose sides are $9cm,12cm$, and $15cm.$

Answer 1

Sides of a triangle are $9cm,12cm,15cm$

Here, $a=9cm,b=12cm,c=15cm$

$\therefore$ Semi-perimeter, $s=\frac{a+b+c}{2}=\frac{9+12+15}{2}=\frac{36}{2}=18$

$\therefore$ Using Heron's Formula, Area of the given triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{18(18-9)(18-12)(18-15)}$

$=\sqrt{18\times 9\times 6\times 3}$

$=\sqrt{9\times 2\times 9\times 2\times 3\times 3}$

$=9\times 3\times 2=54c{m}^2$