Question

The sides of triangle are 6 cm,11 cm and 15 cm.The radius of its incircle is

• A. $\frac{5\sqrt{2}}{4}$ cm
• B. 3$\sqrt{3}$ cm
• C. 6$\sqrt{3}$ cm
• D. $\frac{4\sqrt{2}}{5}$ cm

Answer 1

Answer: (A)

$\frac{5\sqrt{2}}{4}$ cm

Answer 2

From the question we know that, sides of triangle = $a = 6, b = 11, c = 15\ cm$

Area of triangle = $rs$ Here $r$ = radius and $s$ = semi perimeter

$s = \frac{a + b + c}{2}$ = $\frac{6 + 11 + 15}{2}$ = 16 cm

Area of triangle by using Heron's Formula = $\sqrt{s(s - a)(s - b)(s - c)}$

= $\sqrt{16 × 10 × 5 × 1}$ = $20\sqrt{2}\ cm^2$

Radius $r = \frac{\text{area of triangle}}{s}$

$r = \frac{20\sqrt{2}}{16}$ = $\frac{5\sqrt{2}}{4}$

The correct option is (A): $\frac{5\sqrt{2}}{4}$ cm