how long is the diagonal of a piece of paper that is 8.5 in by 11in
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How long is a diagonal tof a paper
To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem, which states that in a right 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 other two sides.
In this case, the length and width of the paper form the two sides of a right triangle, with the diagonal as the hypotenuse. So, you can use the Pythagorean theorem to find the length of the diagonal.
The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In this case, let's assume that the length of the paper is a and the width is b. Using the formula, the length of the diagonal (c) can be found by substituting the values:
c^2 = a^2 + b^2
Here, a is 8.5 inches and b is 11 inches. So, plugging in the values:
c^2 = (8.5)^2 + (11)^2
c^2 = 72.25 + 121
c^2 = 193.25
To find the length of the diagonal (c), take the square root of both sides:
c = √193.25
Using a calculator or a math tool, approximately:
c ≈ 13.89 inches
Therefore, the diagonal of a piece of paper that is 8.5 inches by 11 inches is approximately 13.89 inches.