Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3. Which value of x would make Line segment T V is parallel to Line segment Q S? PLEASE HURRY

9514 1404 393

  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.

Alternate solution

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

(-1,-0.5)

step-by-step explanation: