If two triangles are similar, then the lengths of their corresponding altitudes are proportional to the lengths of their corresponding sides.
8.5
Practice makes perfect
Let's analyze the given triangles.
First, let's notice that two angles of the bigger triangle are congruent to two angles of the smaller triangle.
Therefore, we can say that these triangles are similar by the AA Similarity Theorem.
△_(Bigger) ~ △_(Smaller)
Now, we are given the lengths of the altitudes of the triangles. Recall that if two triangles are similar, the lengths of their corresponding altitudes are proportional to the lengths of their corresponding sides. Using this fact, we can write the following proportion.
7.5/15 = x/17
Let's solve it for x using inverse operations.
