Question

The sides of a triangle are 16 cm, 12 cm and 20 cm. Find the height of triangle, corresponding to the smallest side.

Answer 1

Area of triangle with sides a, b,and c and s $=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides 16 cm, 12 cm and 20 cm, $s=\frac{16+12+20}{2}=24cm$
Area of the triangle with sides 16 cm, 12 cm and 20 cm $=\sqrt{24(24-16)(24-12)(24-20)}=\sqrt{24\times 8\times 12\times 4}=\sqrt{8\times 3\times 8\times 4\times 3\times 4}=8\times 3\times 4=96{cm}^2$

Area of triangle can also be calculated using the formula $\frac{1}{2}\times base\times height$

Let the height for base $12cm$, be h.
So, area $=\frac{1}{2}\times 12\times h=96{cm}^2$

$=>h=16cm$