Answer :

Answer:

LT = 5 , TJ = 30

Step-by-step explanation:

If a line is parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally

TS is parallel ththe side LK and intersects the other two sides JL and JK, then

[tex]\frac{LT}{TJ}[/tex] = [tex]\frac{KS}{JS}[/tex]

note that TJ = 35 - LT and JS = 70 - KS = 70 - 10 = 60

substitute values into the proportion

[tex]\frac{LT}{35-LT}[/tex] = [tex]\frac{10}{60}[/tex] ( cross multiply )

60 LT = 10(35 - LT ) ← divide both sides by 10

6 LT = 35 - LT ( add LT to both sides )

7 LT = 35 ( divide both sides by 7 )

LT = 5

and

TJ = 35 - LT = 35 - 5 = 30