Question

A service station will be built in the highway, and a road will connect it with cray. How long will the new road be?

Answer 1

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,

$\angle ACB\cong \angle CSB$     ( Right angles )

$\angle ABC\cong \angle CBS$      ( Reflexive angles )

Thus, by AA similarity postulate,

$\triangle ACB\sim\triangle CSB$

By the property of similar triangles,

$\frac{AB}{CB}=\frac{AC}{CS}$

$\implies \frac{50}{30}=\frac{40}{x}$

$\implies 50x=30\times 40$

$\implies 50x = 1200$

$\implies x =24$

Thus, the length of the new road = 24 miles