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)

Answer 1

26

Reason: AY = AX = 12 so XY = 24. From △AYB ∼ △XYZ we have AY/XY = AB/XZ = 12/24 = 1/2, so XZ = 2·AB = 10. Angle X is right, so YZ = sqrt(XY^2 + XZ^2) = sqrt(24^2 + 10^2) = sqrt(676) = 26.