Question

The perimeter of a triangle is $50cm$. One side of the triangle is $4cm$ longer than the smaller side and the third side is $6cm$ less than twice the smaller side. Find the area of the triangle.

Answer 1

Let the smallest side of the triangle be $x$ cm long
So, second side $=(x+4)cm$
and third side $=(2x-6)cm$
Given, perimeter $=50cm$
Therefore, $x+(x+4)+(2x-6)=50$
$\Rightarrow 4x=52$
$\Rightarrow x=13cm$
So, first side of the triangle is $13cm$, second side be $17cm$ and third side is $20cm$.
Now, semi-perimeter of the triangle $=\frac{13+17+20}{2}=25cm$
Therefore, area of $\Delta =\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{25(25-13)(25-17)(25-20)}$
$=\sqrt{25\times 12\times 8\times 5}$
= $20\sqrt{30}{cm}^2$