Use the image to answer the question.

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

12 yards
12 yards

15 yards
15 yards

10 yards
10 yards

25 yards

Answer 1

To solve for the length of \( YB \), we can use the properties of similar triangles. Since \( \triangle XYZ \sim \triangle AYB \), the ratios of corresponding sides are equal.

From the similarity, we have: \[ \frac{XY}{AY} = \frac{YZ}{YB} \]

We know the following lengths:

• \( XY = 24 \) yards
• \( YZ = 30 \) yards
• \( YA = 8 \) yards

To find \( YB \), we first need to find \( AY \).

Using the ratio for the similar triangles: \[ AY = YA = 8 \text{ yards} \]

Now we can set up the proportion: \[ \frac{24}{8} = \frac{30}{YB} \]

Cross-multiplying gives us: \[ 24YB = 30 \times 8 \] \[ 24YB = 240 \] \[ YB = \frac{240}{24} = 10 \text{ yards} \]

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