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?

3
8
10
11

Answer 1

Use the Side-Splitter (parallel) theorem: RT/TQ = RV/VS.

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

Answer: 10.