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.

If △XYZ∼△AYB
, and XY¯¯¯¯¯¯¯¯=24
yards, YZ¯¯¯¯¯¯¯=30
yards, and YA¯¯¯¯¯¯¯¯=8
yards, then what is the length of YB¯¯¯¯¯¯¯¯
?

(1 point)
Responses

10 yards
10 yards

12 yards
12 yards

25 yards
25 yards

15 yards

Answer 1

Using the correspondence X↔A, Y↔Y, Z↔B from △XYZ ∼ △AYB, we have XY/AY = YZ/YB. So
YB = (AY·YZ)/XY = (8·30)/24 = 240/24 = 10 yards.

Answer: 10 yards.