Respuesta :
Step 1: For answering this question, we need to recall two important formulas:
A. Formula of the area of a square
B. Formula of the area of a circle
[tex]\text{Area of the square = side length }\ast\text{ side length}[/tex]Step 2: Now, we know that Pam's picture frame area is 3 square feet, now let's use the formula to calculate the side length, as follows:
[tex]\text{ 3 = Side length}^2\text{ }\Rightarrow\text{ }\sqrt{3}\text{ = side length}[/tex]Step 3 : We are ready to calculate the area of Meg's circle picture frame, as follows:
[tex]\text{Area of the circle = }\pi\ast r^2[/tex]If the radius of the picture frame is 1 feet, the area is: 3.14 * 1 * 1 = 3.14 square feet
Step 4: Now, we need to calculate the perimeter of both frames. Let's start with Pam's picture frame. The formula for the perimeter of a square is:
Perimeter of a square = 4 * Side length
We replace the value of the side length, that we calculated on Step 2.
Perimeter of Pam's square = 4 * √3 = 4 * 1.732 = 6.93 feet
Step 5: Finally, we calculate the circumference of Meg's picture frame, using the formula of the circumference, as follows:
[tex]\text{ Circumference of a circle = 2 }\ast\pi\ast r[/tex]Replacing with the values we know:
Circumference = 2 * 3.14 * 1 = 6.28 feet
The correct answer is that the circumference of Meg's picture frame is 6.28 feet and the perimeter of Pam's picture frame by approximately 6.93 feet
