Answer:
x = 3
Step-by-step 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
