Question

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? and can you make it to where I can copy and paste the math

Answer 1

To find the length of the diagonal of a square park using the given information, you can use the formula for the diagonal \( d \) of a square, which is:

\[
d = s \times \sqrt{2}
\]

where \( s \) is the length of the side of the square. According to the problem, the diagonal equals \( 2 - \sqrt{2} \) times the side length.

Here, we have:

1. Side length \( s = 70 \) feet.
2. Using \( \sqrt{2} \approx 1.4 \):

First we can calculate \( \sqrt{2} \) approximated:

\[
\sqrt{2} \approx 1.4
\]

So,

\[
d \approx (2 - 1.4) \times s
\]

Calculating the coefficient:

\[
2 - 1.4 = 0.6
\]

Now plug in the side length:

\[
d \approx 0.6 \times 70
\]

Calculating the diagonal:

\[
d \approx 42 \text{ feet}
\]

Thus, the approximate length from one corner to an opposite corner of the square park is:

\[
\boxed{42 \text{ feet}}
\]

You can copy and paste the math as you requested:

```
d = s * √2
s = 70 feet
√2 ≈ 1.4
d ≈ (2 - 1.4) * s
2 - 1.4 = 0.6
d ≈ 0.6 * 70
d ≈ 42 feet
```