Suppose a railroad rail is 4 kilometers and it expands on a hot day by 12 centimeters in length. approximately how many meters would the center of the rail rise above the ground?

15.49 metres

Step-by-step explanation:

Given in the question that,

the railroad rail is 4 km before expansion.

To find,

the meters the centre of the rail rise above the ground on hot day.

When the railroad expands, it would approximate the forming of an isosceles triangle at the centre of the rail,

with base 4km

and

each isosceles side leg of the triangle is given by

(4 + 12x10^-5) / 2 = 4.00012 / 2 = 2.00006 kilometers

1cm = 10^-2 m = 10^-(2+3) = 10^-5 km

Taking one half of the isosceles triangle, we have a right triangle with base

base  = 4 / 2 = 2 km

and

hypothenuse = 2.00006 kilometers.

By using the Pythagoras theorem, find the height of the right triangle as formed above.

hypo² = base² + height²

2.00006² - 2² = height²

height = √(2.00006² - 2²)

          = 0.01549km

          = 0.01549 x 10^3 m

          = 15.49m  

Thus, the centre of the rail will rise 15.49 metres above the ground.