Please help I always get stuck, some of the steps don't make sense to me ?

If the kid walks for the dotted line, the distance is 36ft.

Now, you can see that this is a triangle rectangle, then we must have that:

x^2 + (x + 6)^2 = 36^2 (the Pythagorean theorem)

Now we must solve this for x.

x^2 + x^2 + 2*6*x + 36 = 36^2

2*x^2 + 12*x -1260 = 0

The solutions for this equation are:

the solutions are:

x = (-12 - 101.1)/4 = -28.78

x = (-12 + 101.1)/4 = 22.3

Then we have x = 22.3 ft

The lenght of the path following the cathetus is:

D = x + x + 6 = 2*22.3ft + 6ft = 50.6ft

Then the difference between the distances is:

Diff = 50.6ft -36ft = 14.6ft