# Thread: another triangle area proof

1. ## another triangle area proof

a triangle ABC is such that AB = 12 and AC = 8. X is the midpoint of the base BC. If the area of the triangle is 72, what is the length of the perpendicular from X to AB and to AC?

thanks
jacs

2. Originally Posted by jacs
a triangle ABC is such that AB = 12 and AC = 8. X is the midpoint of the base BC. If the area of the triangle is 72, what is the length of the perpendicular from X to AB and to AC?

thanks
jacs
Drop a perp from C onto AB, call its length u, then Area(ABC)=12*u/2=72,
so u=12. Then the length of the perp from X onto AB is u/2=6 (similar
triangles).

Drop a perp from B onto AC, call its length v, then Area(ABC)=8.v/2=72,
so v=18. Then the length of the perp from X onto AC is v/2=9 (similar
triangles).

RonL

3. thanks a lot, that works beautifully, appreciate your help.