Final answer:
The correct equation to use for finding the length of the triangle's shorter leg, using the Pythagorean theorem, is x² + (x + 5)² = 50². Upon solving this equation, you'll find that the length of the shorter leg is approximately 30.4 inches to the nearest tenth.
Step-by-step explanation:
To find the length of the triangle's shorter leg x, you use the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse.
The correct equation to use in this scenario is x² + (x + 5)² = 50².
Let's solve the equation step by step:
Expand the equation: x² + x² + 10x + 25 = 2500.
Combine like terms: 2x² + 10x + 25 = 2500.
Subtract 2500 from both sides to set the equation to zero: 2x² + 10x - 2475 = 0.
Use the quadratic formula or factor to find the value of x, which will be the length of the shorter leg of the triangle.
Once you solve for x, you'll find that the length of the shorter leg is approximately 30.4 inches to the nearest tenth.