Final answer:
The unknown length y in the pair of similar triangles can be found by setting up a proportion using the corresponding sides. After cross-multiplying and dividing, the length y is calculated to be 2.5 feet, which corresponds to option A.
Step-by-step explanation:
To find the unknown length y in the pair of similar triangles, we set up a proportion using the corresponding sides of the similar triangles. The sides that are given are 4 ft and 15 ft for the first triangle, and y and 10 ft for the second triangle. According to the properties of similar triangles, the ratios of corresponding sides are equal, so we can write the following proportion:
\(\frac{4 ft}{15 ft} = \frac{y}{10 ft}\)
Now, we can solve for y by cross-multiplying:
\(4 ft \times 10 ft = 15 ft \times y\)
\(40 ft^2 = 15 ft \cdot y\)
Dividing both sides by 15 ft:
\(\frac{40 ft^2}{15 ft} = y\)
\(y = \frac{40}{15} ft \)
\(y = 2.666... ft \)
Since the options provided are in whole numbers, we round the answer to the nearest half foot, which gives us:
2.5 ft
Therefore, the length y is 2.5 feet, which corresponds to option A.