A ramp for loading trucks is 13 feet long and covers 12 feet along the level ground

A ramp for loading trucks is 13 feet long and covers 12 feet along the level ground, as shown below. How many feet high is the highest point on the ramp?

  1. 1
  2. 2
  3. 4
  4. 5
  5. 6 1/4

Answer

The correct answer is D.

The figure is a right triangle with two given side measures. To find the length of the third side, use the Pythagorean theorem: 

(length of the hypotenuse)2 = (length of one side of the triangle)2 + (length of the other side of the triangle)2

In this problem, the 13-foot measure represents the length of the hypotenuse. So, the formula gives the equation

132 = 122 + x2, where x feet is the length of the missing side.

x2 = 132 - 122

x2 = 25

x = ±5

Because the side length of a triangle must be positive, you can ignore the negative solution.