A right triangle can have sides whose lengths are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. The lengths of three sides of a right triangle must satisfy the relationship that the sum of the squares of two sides is equal to the square of the hypotenuse. Write a Java application Project2_PythagoreanTriples_YourName.java to find all Pythagorean triples for side 1, side2 and the hypotenuse, all no larger than 500. Use a triple-nested for loop that tries all possibilities. This method is an example of "brute-force" computing. Note: Brute force refers to a programming style that does not include any shortcuts to improve performance, but instead relies on sheer computing power to try all possibilities until the solution to a problem is found. Sample Output ------Configuration: --- #1 : side1: 3, side2: 4, hypotenuse: 5 #2 : side1: 4, side2: 3, hypotenuse: 5 #3: side1: 5, side2: 12, hypotenuse: 13 #4 : side1: 6, side2: 8, hypotenuse: 10 #5: side1: 7, side2: 24, hypotenuse: 25 #768 : side1: 480, side2: 31, hypotenuse: 481 #769 : side1: 480, side2: 88, hypotenuse: 488 #770 : side1: 480, side2: 108, hypotenuse: 492 #771 : side1: 480, side2: 140, hypotenuse: 500 #772 : side1: 483, side2: 44, hypotenuse: 485 Process completed. Problem Solving Tips 1. This program does not require any input from the user. 2. The formula for the Pythagorean Theorem is hypotenuse? = side 12 + side22. 3. Use brute-force computing techniques try all possible values. 4. Use an if statement to determine whether the sum of the two squared sides is equal to the hypotenuse squared. If so, output side1, side2 and hypotenuse. 5. Use a counter to record the index for each set of Pythagorean triples. 6. Once the program is done, run it and snapshot the whole window to include the both source code and output (the last part only). Save the image to Project2_Pythagorean Triples_YourName.png. 7. If you have any questions as you proceed, ask your lab instructor for assistance. Follow-Up Activities 1. Do not be concerned about trying values that do not make sense, such as a 1-500-1 triangle. That is, skip those sets of side1, side2 & hypotenuse that do not satisfy the following condition a. side 1+side2 > hypotenuse b. side 1-side2]