5 of 105 of 10 Items Question Use the image to answer the question. If △XYZ ∼ △AYB, and YB=25 ft, YA=16 ft, and YZ = 88 ft, then what is the length of YX¯¯¯¯¯¯¯¯ ? (1 point) Responses 67.6 ft. 67.6 ft. 56.32 ft. 56.32 ft. 79 ft. 79 ft. Skip to navigation page 1 of 1

Answer 1

To solve for the length of \( YX \) using the property of similar triangles, we can set up a proportion based on the lengths provided and the similarity of the triangles.

Given:

• \( \triangle XYZ \sim \triangle AYB \)
• \( YB = 25 , \text{ft} \)
• \( YA = 16 , \text{ft} \)
• \( YZ = 88 , \text{ft} \)

According to the properties of similar triangles, the ratios of corresponding sides are equal:

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

Substituting the known values into the proportion:

\[ \frac{YX}{16} = \frac{88}{25} \]

Now we solve for \( YX \):

\[ YX = 16 \cdot \frac{88}{25} \]

Calculating the right side:

\[ YX = \frac{16 \cdot 88}{25} = \frac{1408}{25} = 56.32 , \text{ft} \]

Thus, the length of \( YX \) is \( 56.32 , \text{ft} \).

The correct answer is 56.32 ft.