How many right triangles have a hypotenuse that measures 4x+1 meters and legs that measure 4x-4 meters and x+9 meters? what are the dimensions of the triangles?

Pythagorean theorem of right triangles states that the sum of the square of the legs is equal to the square of the hypotenuse. For this example,
                                 (4x + 1)² = (4x - 4)² + (x + 9)²
Simplifying the equation will give us,
                                  16x² + 8x + 1 = 16x² - 32x + 16 + x² + 18x + 81
Simplifying further,
                                      x² -22x + 96 = 0
The values of x from the equation are 16 and 6. Therefore, there are 2 triangles with the given condition and the dimensions are,
      (16)   :      65 x 60 x 25
      (6)    :      25 x 20 x 15
All dimensions are in meters. 

The sum is 2,160, no problem