9514 1404 393
Answer:
x = 10
Step-by-step explanation:
In order for TV to be parallel to QS, it must divide the sides of the triangle proportionally.
RT/TQ = RV/VS
(x+4)/(x-3) = (x+10)/(x)
1 +7/(x-3) = 1 +10/x . . . . expand each fraction
7/(x -3) = 10/x . . . . . . . . subtract 1
7x = 10(x -3) . . . . . . . . . cross multiply
30 = 3x . . . . . . . . . . . . add 30-7x, simplify
10 = x . . . . . . . . . . . . . . divide by 3
The value of x that makes the segments parallel is 10.
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<em>Alternate solution</em>
You can cross multiply the first fraction we wrote to get ...
x(x +4) = (x -3)(x +10)
x^2 +4x = x^2 +7x -30 . . . eliminate parentheses
30 = 3x . . . . . . subtract x^2+4x-30 from both sides
