Question

The sides of a triangle are $11$ $cm$, $15$ $cm$ and $16$ $cm$. What is the measure of the altitude to the largest side?

• A. $30\sqrt{7}$ $cm$
• B. $30$ $cm$
• C. $\frac{15\sqrt{7}}{4}$ $cm$
• D. $\frac{15\sqrt{7}}{2}$ $cm$

Answer 1

The correct option is C $\frac{15\sqrt{7}}{4}$ $cm$

ar $△ABC=\sqrt{s(s-a)(s-b)(s-c)}$

$S=\frac{a+b+c}{2}=\frac{16+15+11}{2}=21cm$

$\therefore ar△ABC=\sqrt{21(21-16)(21-15)(21-11)}=\sqrt{21\times 5\times 6\times 10}=\sqrt{7\times 3\times 5\times 3\times 2\times 2\times 5}$

$=2\times 3\times 5\sqrt{7}=30\sqrt{7}$

Also, ar $△ABC=\frac{1}{2}\times BC\times h\Rightarrow \frac{1}{2}\times 16\times h=30\sqrt{7}\Rightarrow h=\frac{30\sqrt{7}\times 2}{16}$

$h=\frac{15\sqrt{7}}{4}cm$