Question

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

Answer 1

Each square's ribbon = 4 × side length. Total ribbon for both = 4[(2x^2+1) + (4x−7)] = 4(2x^2+4x−6).

If x = 3.5: inside = 2(3.5)^2 + 4(3.5) − 6 = 24.5 + 14 − 6 = 32.5, so total = 4(32.5) = 130 inches.

Answer: 4(2x^2+4x−6); 130.0 inches (option 4).