Question

Which of the following is the area of a triangle whose sides are 15 m, 16 m and 17 m?

• A. $24\sqrt{4}{m}^2$
• B. $24\sqrt{3}{m}^2$
• C. $24\sqrt{21}{m}^2$
• D. $25\sqrt{2}{m}^2$
• E. None of these

Answer 1

The correct option is C $24\sqrt{21}{m}^2$

Let, a = 15 m, b = 16 m, c = 17 m.
Then, $s=\frac{a+b+c}{2}=\frac{15+16+17}{2}=24m$
$\therefore Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{24(24-15)(24-16)(24-17)}=\sqrt{24\times 9\times 8\times 7}=\sqrt{12096}=24\sqrt{21}{m}^2.$