Question

Triangle R S Q is shown. Angle R S Q is cut by perpendicular bisector l through point S and through midpoint T. The length of line segment R T is x, the length of line segment T Q is 8, the length of line segment Q S is 10, and the length of line segment R S is 10. What is the length of segment TR?

Answer 1

RS = 12

Explanation:

if your question is asking for RS

Answer 2

RT = 8

Explanation:

The given parameters for the triangle are;

The vertices of the given triangle = RSQ

The point on the perpendicular bisector = Pont S and T

The length of the line segment RT = x

The length of the line segment TQ = 8

The length of the line segment QS = 10

The length of the line segment RS = 10

Given that I is a perpendicular bisector that passes through the vertex S, we have;

The line I bisects the segment RQ at point T into equal segments TQ and TR

Therefore, TQ ≅ TR and we have TQ = TR = 8

TR = 8

TR = RT (reflexive property)

Therefore; RT = 8.