A 300 foot long and 300 foot wide playing field is surrounded by a sidewalk. How much distance will you save if you take a short cut and walk diagonally from the corners rather than walking around the sidewalk?
To calculate the distance saved by walking diagonally across the playing field rather than walking around the sidewalk, we can use the Pythagorean theorem.
The length of the field is given as 300 feet, and the width is also 300 feet. Therefore, the distance from one corner to the opposite corner (diagonal) can be found using the Pythagorean theorem:
diagonal² = length² + width²
diagonal² = 300² + 300²
diagonal² = 90,000 + 90,000
diagonal² = 180,000
Taking the square root of both sides gives us the diagonal length:
diagonal = √180,000
diagonal ≈ 424.26 feet
So, by walking diagonally across the playing field, you would save approximately 424.26 feet of distance compared to walking around the sidewalk.