The length of QR of the similar triangles is:
QR = 16
How to find the length of similar triangles?
Two triangles are said to be similar if the ratio of their corresponding sides are congruent.
Using the concept of similar triangles, we have:
Triangle PML is similar to Triangle TRQ
Thus:
PM/TR = ML/RQ
Plugging in the relevant values, we have:
35/14 = (7x - 9)/(2x + 2)
This reduces to:
5/2 = (7x - 9)/(2x + 2)
Cross multiply to get:
5(2x + 2) = 2(7x - 9)
10x + 10 = 14x - 18
14x - 10x = 10 + 18
4x = 28
x = 28/4
x = 7
Thus:
QR = 2(7) + 2
QR = 16