Question

Find PQ if possible

Answer 1

Answer: 11 units

Explanation:

We can say that
`\triangle TSQ\sim\triangle PSR` by AA Similarity Postulate. This is since
`\angle T\cong\angle P` and both ∠TSQ and ∠RSP are right angles, making them congruent.

Similar triangles have a property that corresponding sides are proportional. Hence, we can say that

`(ST)/(PS)=(SQ)/(SR)\\(15)/(PS)=(9)/(12)\\(15)/(PS)=(3)/(4)\\60=3*PS\\PS=20`

We also know that PS is the combined length of PQ and QS. Since we know that QS is 9, let's substitute PQ + 9 in and solve.

`PQ+9=20\\PQ=11`