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

From the calculation, it is clear that the mathematical expression required for both pillows is given as: 4(2x2+4x−6;) 130.0 inches (Options D)

How do we arrive at the above result?

Recall side length is given as: 2x² + 1; and

The Ribbon's side length is: 4x -7.

To determine the length of ribbon required for the two pillows, we must state:

= 4 (2x² +1) + 4(4x-7)

Expanding the bracket since is common to both sides of the expression, we state:

= 4(2x² +1 + 4x -7).

Collecting like terms and resolving sums and differences, we have:

= 4(2x²+ 4x -6).

Step two

Recall that  length is given as x = 3.5 therefore,

substituting x in the equation, we have:

4 (2 * 3.5²) + 4 ((3.5)-6)

= 130 Inches.

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