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The distance of the diagonal can be calculated using the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the other two sides. In this case, the diagonal (d) forms the hypotenuse of a right-angled triangle with the width (w) and length (l) of the field as its sides.
Using the formula:
d^2 = w^2 + l^2
d^2 = 100^2 + 30^2
d^2 = 10000 + 900
d^2 = 10900
Taking the square root of both sides gives:
d = √10900
Therefore, the distance of the diagonal of the soccer field is approximately 104.4 meters.