Question

The lengths of three sides of a triangle are 20 cm, 16 cm and 12 cm. The area of the triangle is
(a) 96 cm²
(b) 120 cm²
(c) 144 cm²
(d) 160 cm²

Answer 1

(a) 96 cm²

$$\begin{gathered} \mathrm{Let}: \\ a=20\mathrm{cm},b=16\mathrm{cm}\mathrm{and}c=12\mathrm{cm} \\ s=\frac{a+b+c}{2}=\frac{20+16+12}{2}=24\mathrm{cm} \\ \mathrm{By}\mathrm{Heron}\text{'}\mathrm{s}\mathrm{formula},\mathrm{we}\mathrm{have}: \\ \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{24(24-20)(24-16)(24-12)} \\ =\sqrt{24\times 4\times 8\times 12} \\ =\sqrt{6\times 4\times 4\times 4\times 4\times 6} \\ =6\times 4\times 4 \\ =96{\mathrm{cm}}^2 \end{gathered}$$