Answer:
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:
[tex]x = \frac{-12 +-\sqrt{12^2 +2*4*1260} }{2*2} = \frac{-12 +-101.1}{4}[/tex]
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
