The altitude of a triangle is how many times the altitude of

The altitude of a triangle is how many times the altitude of a rectangle if the rectangle and the triangle have equal bases and equal areas?

Solution

The area of a rectangle is length * width (A=LW)
The area of a triangle is one-half the base * height (A=1/2bh)
If the triangle area = rectangle area, then
LW=1/2bh
and if b=w,we can substitute b for w, in the equation:
bw=1/2bh
divide both sides by b:
w=1/2h
multiply both sides by 2, to get the answer in terms of the triangle altitude:
2w=h
so the altitude of the triangle is 2 times the altitude of the rectangle.