The diagonal of a square equals 2–√

Question

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 700 feet on a side?(1 point)

Answer 1

To find the diagonal of the square park, you can use the formula that the diagonal \( d \) equals \( s \times \sqrt{2} \), where \( s \) is the side length of the square.

Given that the diagonal equals \( 2 - \sqrt{2} \) times the side length, we can find the diagonal as follows:

1. Calculate \( 2 - \sqrt{2} \) using \( \sqrt{2} \approx 1.4 \): \[ 2 - \sqrt{2} \approx 2 - 1.4 = 0.6 \]

2. Multiply this value by the side length: \[ d \approx 0.6 \times 700 \text{ feet} \]

3. Now multiply to find the length of the diagonal: \[ d \approx 420 \text{ feet} \]

Therefore, the approximate length from one corner to the opposite corner of the square park is 420 feet.