Question

The sides of a triangle measure 13 cm, 14 cm and 15 cm. Its area is

(a) 84 cm²
(b) 91 cm²
(c) 168 cm²
(d) 182 cm²

Answer 1

(a) 84 cm²

Let a = 13 cm, b = 14 cm and c = 15 cm
Then, s = $\frac{a+b+c}{2}$ = $\left(\frac{13+14+15}{2}\right)$ cm = 21 cm
∴ Area of the triangle = $\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)}$ sq. units
= $\sqrt{21\left(21-13\right)\left(21-14\right)\left(21-15\right)}$ cm²
= $\sqrt{21\times 8\times 7\times 6}$ cm²
= $\sqrt{3\times 7\times 2\times 2\times 2\times 7\times 2\times 3}$ cm²
= (2 × 2 × 3 × 7) cm²
= 84 cm²