The diagonal of a square equals 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)
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The length of the diagonal of a square is given by the formula $d = s\sqrt{2}$, where $d$ is the length of the diagonal and $s$ is the length of one side of the square.
We are given that the diagonal of the square is equal to $(2-\sqrt{2})s$. Plugging in the given value for $\sqrt{2}$, we get:
$$d = (2-1.4)s$$
Simplifying, we have:
$$d = 0.6s$$
We are also given that the side length of the square park is 700 feet. So, we can substitute this value for $s$ in the equation to find the length of the diagonal:
$$d = 0.6(700)$$
$$d = 420$$
Therefore, the approximate length from one corner to an opposite corner of the square park is 420 feet.
The given formula for the diagonal of a square is:
diagonal = (2 - √2) * side length
Given that the side length of the square park is 700 feet, we can substitute the values into the formula:
diagonal = (2 - √2) * 700
Now we need to calculate the value of √2 using the given approximation of 1.4:
√2 ≈ 1.4
Substituting this approximation into the formula, we can find the approximate length of the diagonal:
diagonal ≈ (2 - 1.4) * 700
diagonal ≈ 0.6 * 700
diagonal ≈ 420 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 420 feet.