Using the fact that the triangles shown are similar, we can set up a proportion between the lengths of the sides.
The side length in question is QR, or "x". To find its corresponding side in the larger triangle let's look at the similarity.
MNO is similar to PQR Vertices are always written in order of correspondence when stating similarities. Since QR are the last two letters of the triangle's name, and NO are the last two letters of the larger triangle's name, we know that QR and NO are corresponding sides. We can apply this same method to any other side. NO/QR = MN/PQ (MN and PQ are also corresponding sides) Now we can substitute the side names with their values. 4.5/x = 5/2 Cross multiply 5x = 9 Divide both sides by 5 x = 9/5 or 1.8 or 1 4/5
