Question

Find the area of a triangle two sides of which are $8cm$ and $11cm$ and perimeter is $32cm$.

Answer 1

We are given,

Sides of $△ABC$

are $a,b$ & $c\left(incm\right)$

Let $a=8$

$b=11$

here we have perimeter,

i.e., $32cm$.

So, $a+b+c=32cm$

$c=32-(a+b)$

$=32-(8+12)$

$c=32-19$

$c=13cm$

Now, the semi perimeter will be

$S=\frac{perimeter}{2}=\frac{32}{2}=16cm$

Now, Area $=\sqrt{S.(s-a)(s-b)(s-c)}$

$=\sqrt{16(16-8)(16-11)(16-13)}$

$=\sqrt{16\times 8\times 5\times 3}$

$=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 5}$

$=2\times 2\times 2\times \sqrt{2\times 3\times 5}$

Area $=8\sqrt{30}cm\times cm$

Area $=8\sqrt{30}c{m}^2$