College Math Placement Practice Test

What is the distance of the diagonal in yards for a square whose side length is 30 yards?

1. 30√2 yd

2. 60 yd

3. 30 yd

4. 15 yd

The correct answer is: 30√2 yd

To find the distance of the diagonal in a square, you can use the formula derived from the Pythagorean theorem. For a square with side length \(s\), the diagonal \(d\) can be calculated using the formula: \[ d = s\sqrt{2} \] In this case, the side length is given as 30 yards. By substituting this value into the formula, the calculation becomes: \[ d = 30\sqrt{2} \] This result represents the length of the diagonal in yards. The value \( \sqrt{2} \) is approximately 1.414, making the diagonal longer than the length of the sides but still containing the factor of the side length. Thus, when you calculate the diagonal for a square with a side length of 30 yards, the diagonal is indeed: \[ 30\sqrt{2} \text{ yards} \] This aligns perfectly with the answer provided, confirming its accuracy through the geometric properties of squares.