Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3.5?

2x2+4x-6; 22.0 inches

2x2+4x-6; 32.5 inches

4 (2x2+4x-6; ) 88.0 inches

4 (2x2+4x-6; ) 130.0 inches

4 (2x² + 4x - 6); 130.0 inches

Explanation:

The perimeter of the square is the sum of its 4 sides. Since all sides of a square are equal in length, therefore:

Perimeter of square = 4*side length

1 - For the first pillow:

We are given that the side length of the pillow is 2x²+1 in

This means that:

Perimeter of first pillow = 4 (2x²+1) in

2 - For the second pillow:

We are given that the side length of the pillow is 4x-7 in

This means that:

Perimeter of second pillow = 4 (4x-7) in

3 - Total ribbon length required:

The total length of ribbon required to sew both pillows is the summation of the two perimeters

This means that:

Total length required = 4 (2x²+1) + 4 (4x-7)

Taking 4 as a common factor and combining like terms:

Total length required = 4 (2x²+1) + 4 (4x-7)

Total length required = 4 (2x²+1 + 4x-7)

Total length required = 4 (2x² + 4x - 6) in

4 - The length required at x=3.5:

To get the length required, we will simply substitute with x=3.5 in the equation we got in part 3

This is done as follows:

Total length required = 4 (2x² + 4x - 6) in

Total length required = 4 (2 (3.5) ² + 4 (3.5) - 6) in

Total length required = 130.0 in