Question

The difference between the semi perimeter and the side of a $\Delta$ABC arre $8$ cm , $7$ cm and $5$ cm respectively. Find the area of the triangle

Answer 1

Given $s-a=8cm\cdots \left(1\right)$

$s-b=7cm\cdots \left(2\right)$

$s-c=5cm\cdots \left(3\right)$

Where a, b, c are sides of triangle

$s_2$ is 1 semi perimeter ie $s=\frac{a+b+c}{2}$

(1) + (2) + (3)

$\Rightarrow 3s-(a+b+c)=20cm$

$\Rightarrow 3s-\left(25\right)=20cm$

$\Rightarrow s=20cm$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{20(8\times 7\times 5)}=\sqrt{5600}=20\sqrt{14}=59cm$