Question

If △XYZ∼△RST and RS=9, XY=12, and YZ=20, then what does ST equal?

Responses (Options)
( ) 180

( ) 15

( ) 16

Answer 1

Since △XYZ ∼ △RST, corresponding vertices match in order: X↔R, Y↔S, Z↔T. So XY corresponds to RS, giving scale factor k = RS/XY = 9/12 = 3/4.

ST corresponds to YZ, so ST = k·YZ = (3/4)·20 = 15.

Answer: 15.