Recall that if two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.
XV=4
Practice makes perfect
Let's begin with recalling one of the Special Segments of Similar Triangles Theorems.
If two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.
Now, let's look at the given diagram. Let x be the length of XV.
Since we are given that RT and XV are altitudes of △ SRY and △ WXQ, we can create a proportion using the fact that the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.
RT/XV=RY/QX
We can substitute appropriate lengths into the above proportion. Remember that, by the Segment Addition Postulate, the length of RY is the sum of the lengths of RQ and QY, and the length of QX is the sum of the lengths of QY and YX.
5/x=4+6/6+2
Now we will solve the proportion for x using cross multiplication.
