Question

A triangle has sides $5cm,12cm$ and $13cm$. Find the length of the perpendicular from the opposite vertex to the side whose length is $13cm$

Answer 1

$AB\perp BC$

$BD\perp AC$

$Area\left(ABC\right)=\frac{1}{2}\times AB\times BC$ (1)

$Area\left(ABC\right)=\frac{1}{2}\times BD\times AC$ (2)

Equating (1) and (2)

$\frac{1}{2}\times AB\times BC=\frac{1}{2}\times BD\times AC$

Let $AB=12cm,BC=5cm,AC=13cm$

$AB\times BC=BD\times AC$

$12\times 5=BD\times 13$

$BD=\frac{60}{13}$

$BD=4.6cm$

The lengh of the perpendicular from the opposite vertex to the side whose length is 13 cm$=4.6cm$