The pythagorean theorem can only be used with which type of triangle?

Right triangle.

Step-by-step explanation: The Pythagorean theorem can only be used in a right triangle and states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.  

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.