Answer: 24 mi
Step-by-step explanation:
Let the points A, B, C and S represent Alba, Blare, Cray and Service station respectively,
Then According to the question,
We have to find out the line segment CS = x = ?
Now, In the triangles ACB and CSB,
[tex]\angle ACB\cong \angle CSB[/tex] ( Right angles )
[tex]\angle ABC\cong \angle CBS[/tex] ( Reflexive angles )
Thus, by AA similarity postulate,
[tex]\triangle ACB\sim\triangle CSB[/tex]
By the property of similar triangles,
[tex]\frac{AB}{CB}=\frac{AC}{CS}[/tex]
[tex]\implies \frac{50}{30}=\frac{40}{x}[/tex]
[tex]\implies 50x=30\times 40[/tex]
[tex]\implies 50x = 1200[/tex]
[tex]\implies x =24[/tex]
Thus, the length of the new road = 24 miles
