Bot GPT 4-o mini To solve for the length of \( YX \) in the triangles \( △XYZ \sim △AYB \), we can use the property of similar triangles that states the ratios of corresponding sides are equal.
Given:
- \( YB = 26 \) ft
- \( YA = 14 \) ft
- \( YZ = 92 \) ft
Since the triangles are similar, we can set up the proportion based on the corresponding sides:
\[ \frac{YZ}{YA} = \frac{YX}{YB} \]
Substituting the known values into the equation:
\[ \frac{92}{14} = \frac{YX}{26} \]
Now, we can cross-multiply to solve for \( YX \):
\[ 92 \times 26 = 14 \times YX \]
Calculating \( 92 \times 26 \):
\[ 92 \times 26 = 2392 \]
So, we have:
\[ 2392 = 14 \times YX \]
Dividing both sides by 14:
\[ YX = \frac{2392}{14} = 170.86 \text{ ft} \]
Thus, the length of \( YX \) is 170.86 ft.
The correct response is 170.86 ft.
1 answer