College Math Placement Practice Test

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

1. 60√2 yd

2. 90√2 yd

3. 45 yd

4. 30√2 yd

The correct answer is: 30√2 yd

To find the length of the diagonal of a square playground with a given perimeter, we first need to determine the side length of the square. The perimeter of a square is calculated using the formula: \[ \text{Perimeter} = 4 \times \text{side length} \] Given the perimeter of the square is 120 yards, we can set up the equation: \[ 120 = 4 \times \text{side length} \] To find the side length, we divide both sides by 4: \[ \text{side length} = \frac{120}{4} = 30 \text{ yards} \] Next, we use the relationship between the side length and the diagonal of a square. The diagonal \(d\) of a square can be calculated using the formula: \[ d = \text{side length} \times \sqrt{2} \] Substituting the side length we found: \[ d = 30 \times \sqrt{2} \] Thus, the length of the diagonal is: \[ d = 30\sqrt{2} \text{ yards} \] This means the correct answer is that the length of the diagonal is 30√2 yards