Altitudes of Similar Triangles

Altitudes of Similar Triangles

How to find the altitudes (heights) of similar triangles: example and its solution.

Example

If the given triangles are similar, find the value of x. [altitudes of triangles] = x, 5. [sides of triangles] = 8, 6.

It says these two triangles are similar.
So write [ ~ ] between the triangles.

Then their altitudes (heights) and sides
are proportional.

The altitudes are x and 5.
The sides are 8 and 6.

So x/5 = 8/6.

Reduce 8 to 4
and reduce 6 to 3.

Solve the proportion.

Then 3x is equal to, 5⋅4, 20.

Proportion

Divide both sides by 3.

Then x = 20/3.