Question

Find the radius of the incircle of the triangle whose sides measure $4,5$ and $3$ m?

• A. $1$ m
• B. $2$ m
• C. $3$ m
• D. $4$ m

Answer 1

The correct option is A $1$ m

Radius of the incircle $=$ $\frac{2\times areaoftriangle}{a+b+c}$
Perimeter of the triangle, $s=$ $\frac{4+5+3}{2}$ $=6$
Area of triangle $=$ $\sqrt{\left(s\right(s-a\left)\right(s-b\left)\right(s-c\left)\right)}$
$=$ $\sqrt{\left(6\right(6-4\left)\right(6-5\left)\right(6-3\left)\right)}$
$=$ $\sqrt{\left(6\right(2\left)\right(1\left)\right(3\left)\right)}$
$=$ $\sqrt{36}$ $=6$
So, radius of the incircle $=$ $\frac{2\times 6}{12}$
$=1$ m