If the radius of inscribed circle in a right triangle is $3 cm$ and the non-hypotenuse side is $14cm$, calculate triangle's area.

Question

If the radius of an inscribed circle in a right triangle is $3 cm$ and the non-hypotenuse side is $14cm$, calculate triangle's area. I've tried to use the formula: $r= \frac{a+b-c}{2}$ but that doesn't help me that much.

Answer 1

$3=\dfrac{a+14-c}{2}$ $\implies$ $c-a=8$

$a^2+14^2=c^2$ $\implies$ $(c-a)(c+a)=196$

So, $c+a=24.5$ and hence $a=8.25$

$A=\frac12 ab=57.75$.