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 1

Answer: 4.6 mi

Step-by-step 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,

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

$\implies \frac{13}{5}=\frac{12}{x}$

$\implies 13x=5\times 12$

$\implies 13x = 60$

$\implies x =\frac{60}{13}=4.61539\approx 4.6$

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