Answer:
A. 24 miles.
Step-by-step explanation:
We are required,
To find the length of the new road connected to the service station.
Using the theorem stating 'If the altitude is drawn to the hypotenuse of a right triangle, then all the three triangles obtained are similar'.
Thus, the triangles shown in the figure are similar.
Since, when the figures are similar, the proportion of the measurements are equal. We get,
[tex]\dfrac{Perpendicular}{Hypotenuse}=\dfrac{x}{30}=\dfrac{40}{50}[/tex]
Upon solving, we have,
[tex]\dfrac{x}{30}=\dfrac{40}{50}\\\\x=\dfrac{40\times 30}{50}\\\\x=\dfrac{120}{5}\\\\x=24[/tex]
Thus, the length of the new road is 24 miles.
