Question

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
25 yards
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Answer 1

Since triangles \( \triangle XYZ \) and \( \triangle AYB \) are similar, we can set up a proportion based on their corresponding sides.

From the information given, we have:

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

We need to find the length of \( YB \).

Using the property of similar triangles, the ratios of corresponding sides will be equal:

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

Substituting the known values:

\[ \frac{8}{24} = \frac{YB}{30} \]

Now, simplify the left side:

\[ \frac{1}{3} = \frac{YB}{30} \]

Cross-multiply to solve for \( YB \):

\[ 1 \cdot 30 = 3 \cdot YB \]

So,

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

Thus, the length of \( YB \) is 10 yards.