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 options: 24 mi, 30mi, 12mi, 18mi.

Answer 1

Answer: 24 mi

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,

`(AB)/(CB)=(AC)/(CS)`

`\implies (50)/(30)=(40)/(x)`

`\implies 50x=30* 40`

`\implies 50x = 1200`

`\implies x =24`

Thus, the length of the new road = 24 miles