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
Given that the diagonal of a square is equal to 2–√ times the side length, we can write the equation as follows:
Diagonal = (2–√) * Side
Since we know that the side length of the square park is 700 feet, we can substitute this value into the equation:
Diagonal = (2–√) * 700
Now we need to evaluate the value of (2–√) using the given approximation of √2 as 1.4:
Diagonal = (2 – 1.4) * 700
Simplifying, we get:
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.
To find the length of the diagonal of the square park, we can use the given formula:
Diagonal = (√2 - 1) x Side length
Given that the side length of the square park is 700 feet, we can substitute this value into the formula:
Diagonal = (√2 - 1) x 700
Now, let's calculate the approximate value of √2 using the given approximation of 1.4:
√2 ≈ 1.4
Substituting this approximation into the formula:
Diagonal = (1.4 - 1) x 700
Diagonal = 0.4 x 700
Diagonal ≈ 280
Therefore, the approximate length from one corner to an opposite corner of the square park is 280 feet.
To find the length from one corner to the opposite corner of a square park, we can use the Pythagorean theorem since the diagonal forms a right triangle with two sides of the square.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.
Let's represent the length of the diagonal as D and the length of one side of the square as S.
We are given that D = (2 – √2)S.
In this case, the side length of the square park is given as 700 feet, so S = 700 feet.
Substituting the values, we have D = (2 – √2) * 700.
Now, let's find the value of √2 by substituting 1.4 for it.
D = (2 – 1.4) * 700
D = 0.6 * 700
D = 420 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 420 feet.