Final answer:
To find the length of the third side of the triangle, you can use the Pythagorean theorem. Evaluating the given options, the correct answer is 40 inches.
Step-by-step explanation:
The length of the third side of a triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the third side is represented by option C, the square root of 50.
To determine if this is the correct answer, we need to calculate the lengths of the other two sides, square them, and then add them together.
Let's assume that option C is correct and evaluate the triangle:
a² + b² = c²
9² + 5² = 14²
81 + 25 = 196, which is not true.
Therefore, option C is not correct. To find the correct answer, we need to evaluate the other options using the Pythagorean theorem as well.
a² + b² = c²
9² + 40² = ?
81 + 1600 = 1681, which is true.
Therefore, the length of the third side, in inches, is 40 (option D).