6. 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 650 feet on a side?

Answer 1

To find the diagonal of a square given the side length, we can use the formula:

\[ \text{Diagonal} = \text{side length} \times \sqrt{2} \]

Since we are given that the square root of 2 is approximately 1.4, we can rewrite the formula as:

\[ \text{Diagonal} \approx \text{side length} \times 1.4 \]

The side length of the square is given as 650 feet. Thus, we can calculate the diagonal as follows:

\[ \text{Diagonal} \approx 650 \times 1.4 \]

Calculating that gives:

\[ \text{Diagonal} \approx 910 \text{ feet} \]

Now, we need to convert this length from feet to inches. Since there are 12 inches in a foot, we calculate:

\[ 910 \text{ feet} \times 12 \text{ inches/foot} = 10920 \text{ inches} \]

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

\[ \boxed{10920} \text{ inches} \]