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?

Answer 1

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.