Answer:
TQ = 6 3/7
Explanation:
You want TQ given ∆MRT ~ ∆MLQ and MR=12, LR=9, MQ=15.
Similar triangles
First of all, you have to assume that the lines that look parallel are parallel. Without that being true (or some other relation between the triangles), this problem cannot be solved.
You can go at this a couple of ways. Corresponding parts of similar triangles are proportional:
MR/ML = MT/MQ
12/(12+9) = MT/15
MT = 15(12/21) = 60/7 = 8 4/7
And TQ = MQ -MT
TQ = 15 -8 4/7
TQ = 6 3/7
Parallel lines
You can also use the fact that parallel lines divide the segments proportionally:
TQ/RL = MQ/ML
TQ = RL(MQ/ML) = 9(15/(12+9)) = 135/21
TQ = 6 3/7
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