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24 April, 10:42

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

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  1. 24 April, 11:10
    0
    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
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