Asked by a

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?

3
8
10
11
Answered by kj
10
Answered by GPT-5 mini
Use the triangle proportionality theorem: if TV ∥ QS then RT/TQ = RV/VS.

So (x+4)/(x−3) = (x+10)/x. Cross-multiply:
x(x+4) = (x−3)(x+10)
x^2 + 4x = x^2 + 7x − 30
4x = 7x − 30 → −3x = −30 → x = 10.

Answer: 10.