The sides of a triangle are 6 cm, 11 cm and 15cm. The radiusofits incircle is

Sides of the triangle are $$a=6,b=11,c=15$$ cm

Area of a triangle = $$\triangle=rs$$, where $$r$$=in radius and $$s$$ is semi perimeter

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

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

= $$\sqrt{16\times10\times5\times1}$$

= $$\sqrt{2^5\times5^2}=20\sqrt2$$ $$cm^2$$

$$\therefore$$ $$r=\frac{\triangle}{s}$$

= $$\frac{20\sqrt2}{16}=\frac{5\sqrt2}{4}$$ cm

=> Ans - (A)