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

15 yards
15 yards

12 yards
12 yards

25 yards

Answer 1

To find the length of \( YB \) in triangle \( YAB \), we can use the properties of similar triangles since \( \triangle XYZ \sim \triangle AYB \).

The corresponding sides of similar triangles have the same ratio. The ratio can be set up as follows:

\[
\frac{XY}{YA} = \frac{YZ}{YB}
\]

Given:
- \( XY = 24 \) yards
- \( YZ = 30 \) yards
- \( YA = 8 \) yards

First, we can find the ratio using the sides \( XY \) and \( YA \):

\[
\frac{XY}{YA} = \frac{24}{8} = 3
\]

Now we can use this ratio to find \( YB \):

\[
\frac{YZ}{YB} = 3
\]

Substituting the value for \( YZ \):

\[
\frac{30}{YB} = 3
\]

Now, cross-multiply to solve for \( YB \):

\[
30 = 3 \cdot YB
\]
\[
YB = \frac{30}{3} = 10 \text{ yards}
\]

Therefore, the length of \( YB \) is \(\boxed{10 \text{ yards}}\).