How to find the perpendicular distance from B to AC?

Question

"Find the area of triangle $ABC$ with vertices $A(2, 1), B(12, 2) $and $C(12, 8)$. Hence or otherwise, find the perpendicular distance from $B$ to $AC$."

I found the area, which is 30 units by find the length:

$AB:\sqrt101$, $BC: 6$ and $AC: \sqrt149$

But I can't continue, how to find the perpendicular distance from B to AC?

Please help...give me some hint.

Answer 1

Hint: Choose “otherwise“: The distance from $BC$ to $A$ is $10$. Draw a picture to see why.

Answer 2

area of the triangle is given by $bh/2$ where $b$ is the length of the base and $h$ the length of height. Draw a figure of the given triangle and you will see that $b=|AC|$ and $h$ is the length of the required perpendicular. Now put it into the formula for area.