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?

Answer 1

To find the length of ribbon needed for both pillows, we first need to find the perimeter of each pillow.

For the first pillow with side length 2x^2 + 1 inches:
Perimeter = 4(2x^2 + 1) = 8x^2 + 4 inches

For the second pillow with side length 4x - 7 inches:
Perimeter = 4(4x - 7) = 16x - 28 inches

Now, to calculate the total length of ribbon needed for both pillows, we add the perimeters together:
Total length of ribbon = 8x^2 + 4 + 16x - 28
Total length of ribbon = 8x^2 + 16x - 24

If x = 3.5, we can substitute this value into the expression to find the length of ribbon needed:
Total length of ribbon = 8(3.5)^2 + 16(3.5) - 24
Total length of ribbon = 8(12.25) + 56 - 24
Total length of ribbon = 98 + 56 - 24
Total length of ribbon = 130 inches

Therefore, Margot will need 130 inches of ribbon for both pillows if x = 3.5.