If △XYZ ∼ △AYB , and YB=25 ft, YA=16 ft, and YZ = 88 ft, then what is the length of YX¯¯¯¯¯¯¯¯ ? (1 point) Responses 56.32 ft. 56.32 ft. 137.5 ft. 137.5 ft. 79 ft. 79 ft. 67.6 ft. 67.6 ft. Skip to navigation

Answer 1

Given that △XYZ is similar to △AYB (△XYZ ∼ △AYB), we can use the properties of similar triangles to find the length of \( YX \).

We are given the following lengths:

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

From the similarity of the triangles, we have the following proportion involving the sides:

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

Substituting the known lengths into the equation gives us:

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

To find \( YX \), we can cross multiply:

\[ 88 \cdot 16 = 25 \cdot YX \]

Calculating \( 88 \cdot 16 \):

\[ 88 \cdot 16 = 1408 \]

So we have:

\[ 1408 = 25 \cdot YX \]

Now, divide both sides by 25 to solve for \( YX \):

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

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