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.