Answer:the length of the diagonal walkway is 28.3 feet
Explanation:
the area of a square is L^2. A square park is separated into a field area and a playground. These areas are divided by a diagonal walkway. This means that the field area and the playground have equal area. if the area of playground is 200 square feet, it means that the total area if the square park is
200 × 2 = 400 square feet
Therefore, the length of each side of the square park would be
√400 = 20 feet
The diagonal is the hypotenuse of the right angle triangle formed with each side of the square. To determine the diagonal, we would apply pythagoras theorem. It is expressed as
Hypotenuse^2 = opposite side^2 + adjacent side^2.
Therefore
Hypotenuse^2 = 20^2 + 20^2
Hypotenuse^2 = 400 + 400 = 800
Hypotenuse = √800 = 28.3 feet