Question

In the diagram below, TU is parallel to QR. If QS=30, TU=21, and QR=35, find the length of TS. Figures are not necessarily drawn to scale

Answer 1

The length of TS is 12.

Since TU is parallel to QR, we can form a pair of similar triangles:

TSU ~ QSR

From this similarity, we can set up a proportion to find the length of TS:

TS/SU = QS/QR

We know that QS = 30, SU = QR - TU = 35 - 21 = 14, and QR = 35. Plugging these values into the proportion, we get:

TS/14 = 30/35

Solving for TS, we get:

TS = (14 * 30) / 35

TS = 12

Therefore, the length of TS is 12.