College Math Placement Practice Test

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

30√2 yd
60 yd
30 yd
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.