A designer of a sports field wants to find the length of the diagonal of a square lot that is 240 feet on each side Explain how she can calculate this distance rather than measure it.
Pythagorean Theorem applies to right triangles: a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the sides.
For the square lot, the diagonal is the hypotenuse of the triangle, and each side is equal to 240ft.
240^2 + 240^2 = c^2
c = ?
This is a job for the Pythagorean Theorem: a^2 + b^2 = c^2
a = 240
b = 240
c = hyptoneuse (diagnonal of the square)
Can you take it from here?
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To calculate the length of the diagonal of a square lot, we can use the Pythagorean theorem. The Pythagorean theorem 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 square lot forms a right triangle with the diagonal as the hypotenuse and two sides of the square as the other two sides. Let's call the length of the diagonal "d" and the length of one side of the square "s."
According to the Pythagorean theorem, we have the equation:
d^2 = s^2 + s^2
Since each side of the square lot is 240 feet, we substitute "240" for "s" in the equation:
d^2 = 240^2 + 240^2
Now, we simplify and calculate:
d^2 = 57600 + 57600
d^2 = 115200
To find "d," we need to take the square root of both sides:
d = √115200
Using a calculator, we find that:
d ≈ 339.41 feet
Therefore, the length of the diagonal of the square lot is approximately 339.41 feet.