Final answer:
Using the Pythagorean theorem, the diagonal of the table is found to be approximately 38.31 inches, which means none of the provided options are correct.
Step-by-step explanation:
To find the length of the diagonal of the table using the Pythagorean theorem, we will treat the problem as finding the hypotenuse of a right-angled triangle where the width and length of the table are the two shorter sides. We have:
- Width (W) = 22.5 inches
- Length (L) = 31 inches
According to the Pythagorean theorem, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c2 = a2 + b2
In this scenario, this translates to:
Diagonal2 = Width2 + Length2
Diagonal2 = (22.5 inches)2 + (31 inches)2
Diagonal2 = 506.25 inches2 + 961 inches2
Diagonal2 = 147.25 inches2
Now we take the square root of both sides to find the length of the diagonal:
Diagonal = √1467.25 inches2
Diagonal ≈ 38.31 inches
Therefore, none of the options given (1) 25 inches, (2) 33 inches, (3) 37 inches, (4) 41 inches accurately reflect the diagonal length. The correct length of the diagonal, using the Pythagorean theorem, is approximately 38.31 inches.