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

The Correct Option is A

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