JAMB 1994 · UME · Q32

A triangle has base 7 cm and other sides 6 cm and 5 cm. Find its height $h$ onto the base.

Worked solution (try it first)

Find the area with Heron's formula.
The semi-perimeter is $s = \frac{7 + 6 + 5}{2} = 9$ .
Area $= \sqrt{s(s - a)(s - b)(s - c)}$ , which is $\sqrt{9 \times 2 \times 3 \times 4} = \sqrt{216}$ .
As $216 = 36 \times 6$ , the area is $6\sqrt6\text{ cm}^2$ .
Area $= \frac12 \times$ base $\times$ height, so $\frac12 \times 7 \times h = 6\sqrt6$ and $h = \frac{12\sqrt6}{7}$
$= \frac{12}{7}\sqrt6$ cm, option B.