Question

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

Answer options: 40mi, 4.6mi, 5.4mi, 31.2mi

Answer 1

Answer: 4.6 mi

Explanation:

Suppose the points A, B, C and S shows Alba, Blare, Cray and Service station respectively,

Then, 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 (13)/(5)=(12)/(x)`

`\implies 13x=5* 12`

`\implies 13x = 60`

`\implies x =(60)/(13)=4.61539\approx 4.6`

Hence, the approximate length of the new road = 4.6 miles