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
25 yards
25 yards
15 yards
15 yards
10 yards
10 yards
12 yards
To solve this problem, we can set up the ratios of corresponding sides in similar triangles.
In triangle XYZ:
XY/XY = YZ/YA
24/24 = 30/8
1 = 30/8
8 = 30
In triangle AYB:
XY/YB = YZ/YA
24/YB = 30/8
24/YB = 15/4
Cross multiply: 4 * 24 = 15 * YB
96 = 15YB
YB = 96/15
YB = 6.4
Therefore, the length of YB is 6.4 yards.