Question

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

Answer 1

Answer: C. 10

Explanation:

i got it right on the test

Answer 2

9514 1404 393

Answer:

x = 10

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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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