A walkway forms a diagonal of a square playground. The walkway is 24 meters long to the nearest tenth of a meter. How long is the side of the playground?
a square with diagonal d has side length s = d/√2
And the question should have been worded:
The walkway is 24 meters long. To the nearest tenth of a meter, how long is the side of the playground?
To find the length of the side of the playground, we can use the Pythagorean theorem since the walkway forms a diagonal of the square.
The Pythagorean theorem states that for a right triangle, the square 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 walkway forms the hypotenuse of the right triangle, and the two sides of the square are the other two sides.
Let's denote the length of the side of the playground as "x".
Applying the Pythagorean theorem, we have:
x^2 + x^2 = 24^2
Simplifying the equation:
2x^2 = 24^2
Dividing both sides by 2:
x^2 = 24^2 / 2
x^2 = 576 / 2
x^2 = 288
To find the length of the side, we take the square root of both sides:
x = √288
Calculating the square root:
x ≈ 16.9706
Therefore, the length of each side of the playground is approximately 16.9706 meters.