College Math Placement Practice Test

Using the Pythagorean Theorem, what is the value of x if each side of a square playground measures 30 yards?

1. x = 30/2

2. x = 30√2

3. x = 60

4. x = 15√2

The correct answer is: x = 30√2

To determine the value of x using the Pythagorean Theorem in the context of a square playground, we start by understanding the properties of the square. Each side of the square measures 30 yards, and we want to find the length of the diagonal (which can be denoted as x). The diagonal of a square can be derived using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the diagonal, in this case) is equal to the sum of the squares of the other two sides. Since both sides of the square are of equal length, we can apply the theorem as follows: 1. Each side of the square is 30 yards, so the lengths of the two sides that form the right triangle will also each be 30 yards. 2. Applying the theorem, we have: \[ x^2 = 30^2 + 30^2 \] \[ x^2 = 900 + 900 \] \[ x^2 = 1800 \] 3. To find x, we take the square root of both sides: \[ x =