Explain Why the height of a triangle depends on which side you select for the base?
The height of a triangle is the length of the perpendicular
dropped to the base (extended if necessary) from the opposite
vertex. This depends on which side is the base, unless the triangle
is equilateral. For example, if you have a tall skinny isosceles
triangle whose equal sides are a mile long and the third side is an
inch long, the height is about a mile if you choose the third side
as the base. If you choose either of the other two sides as base,
the height will be about an inch.