Final answer:
Using the Pythagorean theorem, we can set up an equation to solve for the shorter leg (x) and then determine the longer leg (2x + 20) and the hypotenuse (2x + 22) of the right triangle.
Step-by-step explanation:
To find the lengths of the sides of a right triangle when given the relationships between the lengths, we can use the Pythagorean theorem which is given by a² + b² = c², where a and b are the lengths of legs and c is the length of the hypotenuse.
Let's denote the length of the shorter leg as x. According to the problem, the longer leg is 20 ft more than twice the shorter leg, so we can express it as 2x + 20 ft. The hypotenuse is given as 22 ft more than twice the length of the shorter leg, represented by 2x + 22 ft.
Applying the Pythagorean theorem, our equation becomes:
x² + (2x + 20)² = (2x + 22)²
Solving this equation will provide the values of x, and subsequently, the lengths of the longer leg and the hypotenuse can be determined.