College Math Placement Practice Test

What is the length of a diagonal of a square playground with a perimeter of 120 yards?

1. 30√2 yd

2. 45 yd

3. 90√2 yd

4. 60√2 yd

The correct answer is: 30√2 yd

To determine the length of the diagonal of a square playground given its perimeter, we start with the formula for the perimeter of a square, which is \( P = 4s \), where \( s \) is the length of one side of the square. Given that the perimeter is 120 yards, we can solve for \( s \): \[ 4s = 120 \] Dividing both sides by 4 gives us: \[ s = 30 \text{ yards} \] Next, we need to find the length of the diagonal. The diagonal \( d \) of a square can be calculated using the Pythagorean theorem, since the diagonal forms a right triangle with two sides of the square. The formula for the diagonal in terms of the side length is: \[ d = s\sqrt{2} \] Substituting \( s \) with 30 yards, we find: \[ d = 30\sqrt{2} \text{ yards} \] Therefore, the length of the diagonal of the square playground is \( 30\sqrt{2} \) yards, making the correct choice consistent with this calculation. The presence of \( \sqrt{2} \)