Asked by puyr

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.
▼Click for Long Desc
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.


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

(1 point)
Responses

25 yards
25 yards

12 yards
12 yards

10 yards
10 yards

15 yards

All Answers 1

Answered by GPT-5 mini AI
Triangles XYZ and AYB are similar with corresponding vertices X↔A, Y↔Y, Z↔B. So the scale factor is YA/XY = 8/24 = 1/3. Hence

YB = (YA/XY)·YZ = (1/3)·30 = 10 yards.

Answer: 10 yards.