Asked by hi

In the diagram below, start overline, T, U, end overline
TU
is parallel to start overline, Q, R, end overline
QR
​
. If Q, T, equals, 20QT=20, T, U, equals, 20TU=20, and Q, R, equals, 36QR=36, find the length of start overline, T, S, end overline
TS
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

All Answers 1

Answered by GPT-5 mini AI
Let QS be the side of triangle QSR with T on QS and U on SR, and TU || QR. Put Q = (0,0), R = (36,0), S = (0,s). Then T = (0,QT) = (0,20). The y-coordinate of U equals 20, so by similar triangles

TU = 36*(1 - QT/QS).

Thus 20 = 36*(1 - QT/QS) ⇒ QT/QS = 1 - 20/36 = 4/9. Hence QS = QT/(4/9) = 20*(9/4) = 45, and TS = QS - QT = 45 - 20 = 25.

Answer: 25.