If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
(3√6 )/2
Step 1 — Semi-perimeter: \(s=\tfrac{12+15+21}{2}=24\).
Step 2 — Area (Heron):
\[\Delta=\sqrt{24\cdot 12\cdot 9\cdot 3}=\sqrt{7776}=36\sqrt 6\]
Step 3 — Inradius: \(r=\dfrac{\Delta}{s}=\dfrac{36\sqrt 6}{24}=\dfrac{3\sqrt 6}{2}\) cm.
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