Question
Mia completely covered a square bulletin using 48 ft^2 of material without any overlap. Which measurement is closest to the side length of this bulletin board in feet?
7
12
6
24
7
12
6
24
Answers
GPT-4o mini
To find the side length of the square bulletin board, we can use the formula for the area of a square, which is:
\[
\text{Area} = \text{side length}^2
\]
In this case, we know the area is 48 ft². So we can set up the equation:
\[
\text{side length}^2 = 48
\]
To find the side length, we take the square root of both sides:
\[
\text{side length} = \sqrt{48}
\]
Now we can simplify \(\sqrt{48}\):
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
Next, we can approximate \(\sqrt{3}\). We know that \(\sqrt{3} \approx 1.732\), so we can calculate:
\[
4\sqrt{3} \approx 4 \times 1.732 \approx 6.928
\]
Now let's compare this value to the given options:
- 7
- 12
- 6
- 24
The value \(6.928\) is closest to \(7\).
Therefore, the measurement closest to the side length of this bulletin board is:
\[
\boxed{7}
\]
\[
\text{Area} = \text{side length}^2
\]
In this case, we know the area is 48 ft². So we can set up the equation:
\[
\text{side length}^2 = 48
\]
To find the side length, we take the square root of both sides:
\[
\text{side length} = \sqrt{48}
\]
Now we can simplify \(\sqrt{48}\):
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
Next, we can approximate \(\sqrt{3}\). We know that \(\sqrt{3} \approx 1.732\), so we can calculate:
\[
4\sqrt{3} \approx 4 \times 1.732 \approx 6.928
\]
Now let's compare this value to the given options:
- 7
- 12
- 6
- 24
The value \(6.928\) is closest to \(7\).
Therefore, the measurement closest to the side length of this bulletin board is:
\[
\boxed{7}
\]