What is the length of pq in the triangles shown below? show your work

21.6

Step-by-step explanation:

If you check the angles in the two triangles, you'd notice that they are the same.

These type of triangles are called similar triangles .

To get the length of the unknown side, you have to compare similar lengths of the two triangles

Line MN is similar to PQ (27 to x)

Line NO is similar to QR (50 to 40)

By comparison, you have

27:50 = x:40

27/50 = x/40 (Cross Multiply)

27 * 40 = x * 50

1080 = 50x (Divide both sides by 50)

x = 1080/50

x = 21.6