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 inches from one corner to an opposite corner of the square that is 700 feet on a side?

Answer 1

To find the length of the diagonal of a square when the side length is given, we can use the relationship given:

\[ \text{Diagonal} = \sqrt{2} \times \text{Side Length} \]

For this problem, we have the side length of the square as 700 feet. Using the approximation \( \sqrt{2} \approx 1.4 \), we can calculate the diagonal:

\[ \text{Diagonal} \approx 1.4 \times 700 \text{ feet} \]

Now, performing the multiplication:

\[ \text{Diagonal} \approx 1.4 \times 700 = 980 \text{ feet} \]

Next, we want to convert this measurement from feet to inches. Since there are 12 inches in a foot, we multiply by 12:

\[ 980 \text{ feet} \times 12 \text{ inches/foot} = 11760 \text{ inches} \]

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

\[ \boxed{11760} \text{ inches} \]