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 70 feet on a side?
The diagonal of a square park with side length 70 feet is calculated using the Pythagorean theorem.
Let's call the length of the diagonal "d" and the side length of the square "s".
According to the given information, the diagonal is equal to 2 times the side length:
d = 2 * s.
Using the Pythagorean theorem, we can write an equation:
d² = s² + s².
Substituting the given values, we have:
d² = 70² + 70².
Simplifying, we get:
d² = 4900 + 4900.
d² = 9800.
To find the approximate length of the diagonal, we take the square root of both sides:
d ≈ √9800.
Since we are using 1.4 as the approximate value for the square root of 2, we can substitute it:
d ≈ 1.4 * √700.
Using a calculator, we find that the square root of 9800 is approximately 99.0.
Therefore, the approximate length in feet from one corner to an opposite corner of the square park is 99.0 feet.
To find the length of the diagonal of a square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length 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 side length of the square park is given as 70 feet. Let's denote this as s.
We are also given that the diagonal of the square equals 2 times the side length, so the diagonal (d) can be represented as:
d = 2s
To find the length of the diagonal, we need to solve for d. Let's substitute the value of s:
d = 2 * 70
d = 140
Therefore, the length of the diagonal is 140 feet.
To find the length from one corner to an opposite corner of a square park, we need to calculate the length of the diagonal.
Given that the diagonal of a square is equal to 2 times the side length, we can use this formula to calculate the length of the diagonal.
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, so the equation becomes:
Diagonal = 2 * side length
Using the equation above, we have:
Diagonal = 2s
Now, we can substitute the given side length of the park, which is 70 feet:
Diagonal = 2 * 70
Diagonal = 140 feet
So, the approximate length from one corner to an opposite corner of the square park is 140 feet.