College Math Placement Practice Test

Question: 1 / 400

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

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 \( \sqrt{2} \)

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