Question
Sonya wants to sew ribbon along each side of a square pillow.
If the pillow has an area of 144 square inches, how much ribbon must she buy to have the exact amount that she needs?
If the pillow has an area of 144 square inches, how much ribbon must she buy to have the exact amount that she needs?
Answers
GPT-4o mini
To find out how much ribbon Sonya needs, we first need to determine the perimeter of the square pillow. The area of the pillow is given as 144 square inches.
We know that the area \( A \) of a square is given by the formula:
\[
A = s^2
\]
where \( s \) is the length of one side of the square. To find the side length, we can set up the equation:
\[
s^2 = 144
\]
Taking the square root of both sides, we find:
\[
s = \sqrt{144} = 12 \text{ inches}
\]
Now that we have the side length, we can calculate the perimeter \( P \) of the square pillow. The perimeter of a square is given by the formula:
\[
P = 4s
\]
Substituting the side length we found:
\[
P = 4 \times 12 = 48 \text{ inches}
\]
Therefore, the total amount of ribbon that Sonya must buy to sew along each side of the pillow is:
\[
\boxed{48} \text{ inches}
\]
We know that the area \( A \) of a square is given by the formula:
\[
A = s^2
\]
where \( s \) is the length of one side of the square. To find the side length, we can set up the equation:
\[
s^2 = 144
\]
Taking the square root of both sides, we find:
\[
s = \sqrt{144} = 12 \text{ inches}
\]
Now that we have the side length, we can calculate the perimeter \( P \) of the square pillow. The perimeter of a square is given by the formula:
\[
P = 4s
\]
Substituting the side length we found:
\[
P = 4 \times 12 = 48 \text{ inches}
\]
Therefore, the total amount of ribbon that Sonya must buy to sew along each side of the pillow is:
\[
\boxed{48} \text{ inches}
\]