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?

Answer 1

Step-by-step explanation:

$perimeter \: of \: first \: pillow \: is \: \\ 4(2 {x}^{2} + 1) \\ perimeter \: of \: second \: pillow \: is \: \\ 4(4x - 7) \\ so \: we \: need \: compeletly \: 4(2 {x}^{2} + 1) + 4(4x - 7) \: ribbons. \\ 8 {x}^{2} + 4 + 16x - 28 = 8 {x}^{2} + 16x - 24 = \\ 8( {x}^{2} + 2x - 3) = 8(x + 3)(x - 1) \\ 8(3.5 + 3)(3.5 - 1) = 8(6.5)(2.5) = 8 \times 2.5 \times 6.5 = 20 \times 65 \times {10}^{ - 1} = 1300 \times {10}^{ - 1} = 130 \\ and \: we \: are \: done.$

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