Question

In the diagram below, ST is parallel to PQ. If PS = 15, ST = 20, and PQ = 32, find the length of SR. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.​

Answer 1

To find the length of SR, set up a proportion using the lengths of the corresponding sides of two similar triangles STQ and SRP.

Step-by-step explanation:

To find the length of SR, we can use the property of parallel lines that states corresponding angles are congruent. Since ST is parallel to PQ, angle TSR is congruent to angle SPQ.

We can set up a proportion using the lengths of the sides. Since SR and PQ are corresponding sides of two similar triangles (STQ and SRP), we have:

(SR / ST) = (PQ / PS)

Substituting the given values, we get:

(SR / 20) = (32 / 15)

Cross-multiplying and solving for SR, we get SR = 32 * 20 / 15 = 42.67