Question

The area of a triangle whose sides are 8 cm, 10 cm and 14 cm is equal to

• A. $36\sqrt{3}c{m}^2$
• B. $20\sqrt{2}c{m}^2$
• C. $16\sqrt{6}c{m}^2$
• D. $8\sqrt{6}c{m}^2$

Answer 1

The correct option is C $16\sqrt{6}c{m}^2$

Let the sides of the triangle be a = 8 cm, b = 10 cm and c = 14 cm.
$\therefore$ Semiperimeter, (s) $=\frac{a+b+c}{2}$
$=\frac{8+10+14}{2}$
=16 cm
$\therefore$ Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{16(16-8)(16-10)(16-14)}$
$=\sqrt{16\times 8\times 6\times 2}$
$=\sqrt{8\times 2\times 8\times 6\times 2}$
$=8\times 2\times \sqrt{6}$
$=16\times \sqrt{6}c{m}^2$
Hence, the correct answer is option (c).