Question

△NPQ is similar to △RST

NP=3 inches, PQ=5 inches, and RS=10.5 inches.
What is ST?
Enter your answer as a decimal in the box.
____in

Answer 1

17.5

Explanation:

If the triangles are similar, then the corresponding sides exist in proportion to one another. Side NP in the one triangle is corresponding and therefore, proportionate to side RS in the other triangle. Side PQ is corresponding to side ST. Set up a ratio (proportion) as follows (but this is not the only way):

`(NP)/(PQ)=(RS)/(ST)`

and fill those in with the proper side lengths:

`(3)/(5)=(10.5)/(ST)`

Cross multiply to get

3 ST = 52.5

and ST = 17.5