A park is shaped like a rectangle with a length 5 times it's width w. What is a simplified expression for the distance between opposite corners of the park?
sqrt(w^2 + 25 w^2) = w sqrt (26)
To find the distance between opposite corners of the park, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 lengths of the other two sides.
In this case, the park is in the shape of a rectangle, and we can consider the distance between opposite corners as the hypotenuse of a right-angled triangle, with the two sides being the length and width of the rectangle.
Let's denote the width of the park as w. Since the length of the park is 5 times its width, the length can be expressed as 5w.
Now, applying the Pythagorean theorem, the distance between opposite corners of the park can be found as follows:
Distance^2 = Length^2 + Width^2
Distance^2 = (5w)^2 + w^2
Distance^2 = 25w^2 + w^2
Distance^2 = 26w^2
Therefore, the simplified expression for the distance between opposite corners of the park is √(26w^2).