In the diagram below of triangle PQR, S is the midpoint of PR and T is the midpoint of QR. If ST = -32 + 9x, and PQ = -53 +28, what is the measure
of ST?

ST=?

ST = 4

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle is half the length of the third side.

ST = PQ substitute values

- 32 + 9x = (- 5x + 28) ← multiply both sides by 2 to clear the fraction

- 64 + 18x = - 5x + 28 (add 5x to both sides )

- 64 + 23x = 28 ( add 64 to both sides )

23x = 92 ( divide both sides by 23 )

x = 4

Then

ST = - 32 + 9x = - 32 + 9(4) = - 32 + 36 = 4