Final answer:
Using the Pythagorean theorem, we calculate that the length of the diagonal of a standard sheet of printer paper measuring 8.5 inches by 11 inches is approximately 13.9 inches to the nearest tenth of an inch.
Step-by-step explanation:
To determine the length of the diagonal of a standard sheet of printer paper that measures 8.5 inches by 11 inches, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). When we apply this to the dimensions of the paper, we can set up the equation:
a² + b² = c²
where a is the width of the paper (8.5 inches), b is the length of the paper (11 inches), and c is the diagonal of the paper. Plugging in the numbers, we get:
8.5² + 11² = c²
72.25 + 121 = c²
193.25 = c²
Taking the square root of both sides gives us the length of the diagonal:
c = √193.25
c ≈ 13.9 inches (rounded to the nearest tenth of an inch)
Therefore, the length of the diagonal of the standard sheet of printer paper is approximately 13.9 inches to the nearest tenth of an inch.