Question

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

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

Answer 1

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

By Heron's formula, we have area of triangle
$=\sqrt{S(S-a)(S-b)(S-c)}$

Here, $S=\frac{11+15+16}{2}=\frac{42}{2}=21cm$

$\therefore$ Area of triangle $=\sqrt{21\left(10\right)\left(6\right)\left(5\right)}$

$=30\sqrt{7}$ sq cm

Also, Area of triangle = $\frac{1}{2}\times base\times height$

$\therefore$ height $=\frac{2\times area}{base}=\frac{30\sqrt{7}}{8}$

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