Question

The sides of a triangle are 16cm,12cm and20cm.
I) Find the area of the triangle
II) height of the triangle, corresponding to the largest side.
III) height of the triangle, corresponding to the smallest side.

Answer 1

$\textbf{ \huge{ Hello Mate! }}$

We will use heron's formula to solve this solution. Hence, heron's formula is

$= \sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{16 + 12 + 20}{2} = 24 \: cm \\ = \sqrt{24(24 - 16)(24 - 20)(24 - 12)} \\ = \sqrt{ {2}^{3} \times 3 \times {2}^{3} \times {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ = 96 \: {cm}^{2}$
$\boxed{ \textsf{ \red{ Area\:is\:96\:sq\:cm }}}$

$ii)area = \frac{1}{2} \times b \times h \\ 96 = \frac{1}{2} \times 20 \times h$
$\boxed{ \textsf{ \red{ Height\:is\:9.6cm}}}$

$iii)96 = \frac{1}{2} \times 12 \times h$
$\boxed{ \textsf{ \red{ Height\:is\:16cm }}}$

Have great future ahead!