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27 votes
Find x. Hint: Use Similar Triangles.

Find x. Hint: Use Similar Triangles.-example-1
User Acushner
by
2.2k points

1 Answer

17 votes
17 votes

Answer:

x = 3

Explanation:

The similar triangles are ...

∆PMT ~ ∆PKL

Corresponding sides are proportional, so we have ...

PM/MT = PK/KL

6/7 = (6+x)/10.5

Multiplying by 21 gives ...

18 = 12 +2x

9 = 6 +x . . . . . . divide by 2

x = 3 . . . . . . . . subtract 6

__

Alternate solution

Locate point S on KL such that TS || MK. Then KS = 7 and SL = 3.5. Now, the proportion can be written as ...

MK/SL = PM/MT

x/3.5 = 6/7

x = (3.5/7)6 = 3 . . . . multiply by 3.5 and simplify

User Olavi Mustanoja
by
3.1k points