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How do i solve this?

How do i solve this?-example-1

1 Answer

6 votes

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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