Similarity of Heights (Altitudes) in Triangles

Similarity of Heights (Altitudes) in Triangles

How to solve the similarity of heights (altitudes) in triangles problems: example and its solution.

Example

If triangle ABC ~ triangle A'B'C', find the value of x. The measure of the side of the left triangle: 6. The measure of the height of the left triangle: 5. The measure of the side of the right triangle: 8. The measure of the height of the right triangle: x.

If two triangles are similar,
then their heights are proportional.

So the heights and the sides are proportional:
5 / x = 6 / 8.