Question

Use the image to answer the question.

Triangle upper Y upper X upper Z is divided into triangle upper Y upper B upper A and quadrilateral upper A upper B upper Z upper X by horizontal line upper A upper B.

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

YZ = 26

Reason: AY = AX = 12 so XY = AY + AX = 24. From similarity AYB ∼ XYZ the scale factor is XY/AY = 24/12 = 2, so XZ = 2·AB = 2·5 = 10. Triangle XYZ is right at X, so YZ = sqrt(XY^2 + XZ^2) = sqrt(24^2 + 10^2) = sqrt(676) = 26.