Question

a square rug has an area 100 ft². write the side length as a square root. then decide if the side length is a rational number.
the rug has side length
ft.

Explanation:

Step1: Recall area of square formula

The area \( A \) of a square is given by \( A = s^2 \), where \( s \) is the side length.

Step2: Substitute area value

We know \( A = 100 \, \text{ft}^2 \), so substitute into the formula: \( 100 = s^2 \).

Step3: Solve for side length

To find \( s \), take the square root of both sides: \( s=\sqrt{100} \).

Step4: Simplify the square root

Since \( 10\times10 = 100 \), \( \sqrt{100}=10 \).

Answer:

The rug has side length \( \boldsymbol{10} \) ft. (And \( \sqrt{100} = 10 \), which is a rational number as it can be expressed as \( \frac{10}{1} \).)