A road starts at sea level and climbs steadily, reaching an elevation of 2000 feet after 8 miles, as shown in the diagram.
8 mi
5 mi
2000 ft
Note: Figure is not drawn to scale.
What is the elevation in feet of the road 5 miles from the starting point?
A. 1000
B. 1250
C. 750
D. 1500

Answer:

I think the answer is 1500

Step-by-step explanation:

 Elevation of the road at 5 miles from the starting point is 1250 ft.

Given in the question,

Two triangles formed by a road are ΔADE and ΔABC (As shown in the figure attached).

Since, ∠A ≅ ∠A (Reflexive property)

           ∠AED ≅ ∠ACB (right angles)

            ΔADE ~ ΔABC (By A-A property of similarity)

In these similar triangles, corresponding sides will be proportional.

[tex]\frac{AB}{BC}=\frac{AD}{DE}[/tex]

[tex]\frac{8}{2000}=\frac{5}{DE}[/tex]

[tex]DE=\frac{5\times 2000}{8}[/tex]

      [tex]=1250[/tex] miles

   Therefore, elevation of the road at 5 miles from the starting point will  be 1250 ft.

    Option (B) will be the answer.

Learn more about the similarity of the triangles here,

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