The diagonal of a square equals sqrt(2) times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side? (1 point)
The diagonal of a square can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (sides of the square).
Let's denote the side length of the square as s. According to the given information, the diagonal of the square is √2 times the side length.
Therefore, the equation becomes:
diagonal^2 = (√2 * s)^2
Simplifying,
diagonal^2 = 2s^2
Taking the square root of both sides,
diagonal = √(2s^2)
diagonal = √2 * s
Now, using s = 700 feet, we can calculate the approximate length of the diagonal:
diagonal = √2 * 700
diagonal ≈ 1.4 * 700
diagonal ≈ 980 feet
Therefore, the approximate length in feet from one corner to an opposite corner of the square park is 980 feet.
To find the length from one corner to an opposite corner of the square park, we need to multiply the side length by the square root of 2.
Given that the side length of the square park is 700 feet, and using 1.4 as the approximate value for the square root of 2, we can calculate the length as follows:
Length = Side length x Square root of 2
= 700 ft * 1.4
= 980 ft
Therefore, the approximate length from one corner to an opposite corner of the square park is 980 feet.