Triangles ABC and XYZ are similar, with A corresponding to X and B to Y. If AB=3, BC=4, and XY=5, then YZ is

1988 AMC 12 Problem 2

Attempt Problem 2 of the 1988 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 12 solutions, or check the answer key.

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Triangles

ABC

and

XYZ

are similar, with

A

corresponding to

X

and

B

Y.

AB=3,

BC=4,

and

XY=5,

then

YZ

3\frac34

6

6\frac14

6\frac23

8

Match

AB

with

XY

and

BC

with

YZ

Use the scale factor from the first triangle to the second

The scale factor is

\frac{XY}{AB}=\frac{5}{3}.

Therefore

YZ=(\frac{5}{3})BC=(\frac{5}{3})(4)

and

YZ=\frac{20}{3}=6\frac23.

Thus the correct answer is D.