a square park is separated into a field area and a playground. these areas are divided by a diagonal walkway. if the area of playground is 200 square feet, how long is the diagonal walkway?

Question

Mathematics

Rigoberto Harrell

2 July, 15:55

a square park is separated into a field area and a playground. these areas are divided by a diagonal walkway. if the area of playground is 200 square feet, how long is the diagonal walkway?

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Answers (1)

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Laurel Roman · Answer 1

Answer:the length of the diagonal walkway is 28.3 feet

Step-by-step 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