Question

The in-radius of a triangle whose sides are given by $3,5,6$ is?

• A. $\sqrt{8/7}$
• B. $\sqrt{8}$
• C. $\sqrt{7}$
• D. $\sqrt{7/8}$

Answer 1

Answer: (A)

$\sqrt{8/7}$

We know, $s=\frac{a+b+c}{2}$

$s=\frac{3+5+6}{2}$

$\therefore s=7$

Also, $\Delta =\sqrt{s(s-a)(s-b)(s-c)}$

Therefore, $\Delta =\sqrt{7\times 4\times 2\times 1}=2\sqrt{14}$

$\therefore r=\frac{\Delta }{s}=\frac{2\sqrt{14}}{7}=\sqrt{\frac{8}{7}}$