A rectangular field is 25 yards wide and 50 yards long. Patrick walks diagonally across the field. How far does he walk? Round to the nearest hundredth.
To find the distance Patrick walks when walking diagonally across the field, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the length and width of the field form the two sides of the right triangle, and the distance Patrick walks forms the hypotenuse.
Let's call the distance Patrick walks "d." So, using the Pythagorean theorem:
d^2 = 25^2 + 50^2
d^2 = 625 + 2500
d^2 = 3125
d = √3125
d ≈ 55.90
Therefore, Patrick walks approximately 55.90 yards when walking diagonally across the field.