Question
Mia completely covered a square bulletin board using 48 ft2 of material without any overlap. Which measurement is closest to the side length of this bulletin board in feet?
Responses
A 7 ft7 ft
B 12 ft12 ft
C 6 ft6 ft
D 24 ft
Responses
A 7 ft7 ft
B 12 ft12 ft
C 6 ft6 ft
D 24 ft
Answers
GPT-4o mini
To find the side length of the square bulletin board, we can first find the side length using the area formula for a square, which is:
\[
\text{Area} = \text{side length}^2
\]
Given that the area is 48 ft², we can set up the equation:
\[
\text{side length}^2 = 48
\]
To find the side length, we take the square root of both sides:
\[
\text{side length} = \sqrt{48}
\]
Calculating this:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
Approximating \(\sqrt{3} \approx 1.732\):
\[
4\sqrt{3} \approx 4 \times 1.732 = 6.928
\]
So, the side length of the bulletin board is approximately 6.928 feet. The closest whole number from the responses given is:
**A: 7 ft**.
\[
\text{Area} = \text{side length}^2
\]
Given that the area is 48 ft², we can set up the equation:
\[
\text{side length}^2 = 48
\]
To find the side length, we take the square root of both sides:
\[
\text{side length} = \sqrt{48}
\]
Calculating this:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
Approximating \(\sqrt{3} \approx 1.732\):
\[
4\sqrt{3} \approx 4 \times 1.732 = 6.928
\]
So, the side length of the bulletin board is approximately 6.928 feet. The closest whole number from the responses given is:
**A: 7 ft**.