Question

The South Memorial School is designing a new playground, and there will be a walkway that diagonally crosses the square playground. The walkway is 55 meters long.

Part I: Include a sketch of the playground and find the length of one side. Round your answer to the nearest 10th.
a) 19.5 meters
b) 27.1 meters
c) 39.1 meters
d) 62.2 meters

Answer 1

To find the length of one side of the playground, we can use the Pythagorean theorem to calculate the square of the side length. By solving the equation, we find that the length of one side of the playground is approximately 39.1 meters.

Step-by-step explanation:

To find the length of one side of the playground, we need to use the concept of Pythagorean theorem. Since the walkway diagonally crosses the square playground, the walkway will form a right triangle with one of the sides of the square playground. Let's assume the length of one side of the square playground is 'x'.

According to the Pythagorean theorem, the square of the hypotenuse (walkway) is equal to the sum of the squares of the other two sides (one side of the playground).

x^2 + x^2 = 55^2

2x^2 = 55^2

x^2 = 55^2 / 2

x = √(55^2 / 2)

x = √(3025 / 2)

x ≈ √(1512.5)

x ≈ 39.1 ≈ ≈ 39.1 meters (rounded to the nearest 10th)