How do you do this problem

Question

Suppose a railroad rail is

55

kilometers and it expands on a hot day by

1414

centimeters in length. Approximately how many meters would the center of the rail rise above the​ ground?

Answer 1

The correct answer of this problem is fairly complex. I'm not sure if you are are in an advanced math class or not but a first order answer is to use the Pythagorean Theorem as noted in the other answer.

A more correct answer is to realize that, if the railroad track is constrained at each end of the 55 km length and if it is unconstrained (allowed to bow up) everywhere else, it would form an inverted hyperbolic cosine shape that would match the equation y = a cosh (x/a) but I doubt if your teacher expects you to utilize this complex solution.

Answer 2

Use Pythagoras, Draw and label a diagram!

7 cm = 0.07 m

0.07 m = 0.00007 km

h² = (55 + 0.00007)² - 55²

Can you determine h and answer?