Discussion

Explanation:

s = (a + b + c)/2

where s is the semi-perimeter and a, b and c are the sides of the triangle.

s = (6 + 8 + 10)/2 = 12 cm

Area = $\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)}$

        = $\sqrt{12\left(12-6\right)\left(12-8\right)\left(12-10\right)}=\sqrt{12\times 6\times 4\times 2}$

        = 24

Alternately,

6, 8 and 10 are pythagorean triplets i.e. 10² = 8² + 6²

⇒ The given triangle is a right triangle

⇒ Area = ½ × 6 × 8 = 24

Hence, option (b).

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