If a rectangular structure measures 56 feet by 90 feet, what is the diagonal measurement, assuming all corners are square?

To find the diagonal measurement of a rectangular structure, the Pythagorean theorem is used. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (which, in this case, is the diagonal of the rectangle) is equal to the sum of the squares of the lengths of the other two sides.

For this rectangle measuring 56 feet by 90 feet, you can set up the equation as follows:

1. Square the lengths of each side:

• 56 feet squared = 3136

• 90 feet squared = 8100

2. Add these two values together:

• 3136 + 8100 = 11236

3. Now, take the square root of this sum to find the diagonal:

• √11236 = 106 feet

Thus, the diagonal measurement of the rectangular structure is 106 feet. This is the correct answer since it adheres directly to the application of the Pythagorean theorem, showcasing how the relationship between the sides of a rectangle functions mathematically to yield the length of the diagonal.