Final answer:
To solve this problem, assign variables to represent the lengths of the legs and hypotenuse. Use the Pythagorean theorem to set up an equation and solve for the variable. Substitute the value of the variable back into the expressions to find the lengths of the sides of the right triangle.
Step-by-step explanation:
To solve this problem, let's assign variables to represent the lengths of the legs and hypotenuse. Let x be the length of the shorter leg.
According to the given information, one leg is 7 inches more than four times the length of the other leg. So, the longer leg is 4x + 7 inches.
The hypotenuse is 9 inches more than the shorter leg. Therefore, the hypotenuse is x + 9 inches.
Now, we can use the Pythagorean theorem to solve for x:
x^2 + (4x + 7)^2 = (x + 9)^2
Solving this equation will give us the value of x and we can then substitute it back into the expressions to find the lengths of the legs and hypotenuse.
After solving the equation, we find that x = 3. Substituting this value, we get the lengths of the legs as 3 inches and 19 inches, and the length of the hypotenuse as 12 inches. Therefore, the correct answer is option d) Legs: 10 inches and 47 inches; Hypotenuse: 56 inches.