Question

Point upper A is on line upper Y upper X. Point upper B is on diagonal upper Y upper Z. A small square box is marked in angle upper A and angle upper X.


Image Long DescriptionPoint upper A is on line upper Y upper X. Point upper B is on diagonal upper Y upper Z. A small square box is marked in angle upper A and angle upper X.

If △AYB∼△XYZ
, AB=5
, AY=12
, and AY=AX
, what is the length of YZ
?

(1 point)
YZ=

Answer 1

Since △AYB ∼ △XYZ with A↔X, Y↔Y, B↔Z, we have XY/AY = scale factor. AY = AX = 12 so XY = 12+12 = 24, hence scale = 24/12 = 2.

In right △AYB (right at A), YB = sqrt(AY^2+AB^2) = sqrt(12^2+5^2) = 13. Thus YZ = 2·YB = 2·13 = 26.

YZ = 26