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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 YB=25 ft, YA=16 ft, and YZ = 88 ft, then what is the length of YX¯¯¯¯¯¯¯¯ ?

(1 point)
Responses

79 ft.
79 ft.

56.32 ft.
56.32 ft.

137.5 ft.
137.5 ft.

67.6 ft.

Answer 1

To find the length of \( YX \), we can use the information about the similar triangles \( \triangle XYZ \sim \triangle AYB \).

The sides of similar triangles are proportional, which gives us the following relationship:

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

We can plug in the values we have:

• \( YA = 16 \) ft
• \( YB = 25 \) ft
• \( YZ = 88 \) ft

Now substituting these values into the proportion:

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

To find \( YX \), we'll solve for it:

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

Calculating the right-hand side:

\[ YX = 16 \times 3.52 = 56.32 \text{ ft} \]

Thus, the length of \( YX \) is:

56.32 ft.