Question 23

If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?

Solution

Semi perimeter, S= $$\frac{15+21+12}{2}=24.$$

Area, A=$$\sqrt{24\left(24-15\right)\left(24-21\right)\left(24-12\right)}=\sqrt{24\times3\times9\times12}=36\sqrt{6}.$$

So, inradius, r= $$\frac{A}{S}=\frac{36\sqrt{6}}{24}=\frac{3\sqrt{6}}{2}.$$

C is correct choice.

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