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 applied, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal, in this case) is equal to the sum of the squares of the lengths of the two other sides.

In this scenario, the sides of the rectangle are 56 feet and 90 feet. According to the Pythagorean theorem:

Diagonal² = Side 1² + Side 2²

Diagonal² = 56² + 90²

Diagonal² = 3136 + 8100

Diagonal² = 11236

To find the length of the diagonal, take the square root of 11236:

Diagonal = √11236 ≈ 106 feet.

Therefore, the diagonal measurement of the structure is indeed 106 feet. This calculation confirms that the choice of 106 feet is the correct answer, as it accurately represents the diagonal length determined by applying the Pythagorean theorem to the given dimensions of the rectangular structure.