Problem: Assume one leg of a right triangle is twice as long as the other leg. If the hypotenuse of the triangle is 12 meters, find the lengths of the two legs.

Solution: Let the legs be x and 2x.

        a² + b² = c²              Pythagorean Theorem.

        x² + (2x)² = 12²       Substitution

        x² + 4x² = 144         Simplification

        5x² = 144        

        x² = 144/5
                           

Extract the positive square root and rationalize the denominator.

                                           
        
        x = 5.37 (approximately)