Given the soccer field with length of 84m and width of 35 m what is the distance of the diagonal of the field
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Well, let me grab my measuring tape... Just kidding! Who needs to measure when we have math? So, to find the diagonal of a rectangle, we can use the good old Pythagorean theorem, which states that the square of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides. In this case, the length and width are the other two sides. So, the diagonal (d) can be calculated using the formula √(length^2 + width^2). Plugging in the values, we get √(84^2 + 35^2). Crunching the numbers... and the result is approximately 91.13 meters. Voila!
To find the distance of the diagonal of the soccer field, you can use the Pythagorean theorem, which states that in a right triangle, the square 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 soccer field form the two sides of a right triangle, and we can find the length of the diagonal (the hypotenuse) using the formula:
diagonal² = length² + width²
Given that the length of the field is 84m and the width is 35m, we can substitute these values into the formula:
diagonal² = (84m)² + (35m)²
Simplifying the equation:
diagonal² = 7056m² + 1225m²
diagonal² = 8281m²
Taking the square root of both sides:
diagonal = √8281m²
Calculating the square root:
diagonal ≈ 91m
Hence, the distance of the diagonal of the soccer field is approximately 91 meters.
To find the distance of the diagonal of the soccer field, we can use the Pythagorean theorem. The theorem 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 other two sides.
In the soccer field, the length and the width form the two sides of the right triangle, with the diagonal being the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 84^2 + 35^2
Diagonal^2 = 7,056 + 1,225
Diagonal^2 = 8,281
To find the length of the diagonal, we need to take the square root of both sides:
Diagonal = √8,281
Using a calculator or math software, we find that the square root of 8,281 is approximately 91.02.
Therefore, the distance of the diagonal of the soccer field is approximately 91.02 meters.
use the pythagorean theorem
If the diagonal has length x, then
x^2 = 35^2 + 84^2
You can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.