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 4xâÂ’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 4xâÂ’6; 22. 0 inches 2x2 4xâÂ’6; 32. 5 inches 4(2x2 4xâÂ’6;) 88. 0 inches 4(2x2 4xâÂ’6;) 130. 0 inches.

Answer 1

The expression used for the length of ribbon that she needs for both pillows will be $4(2x^{2} +4x-6)$.

The total length of the pillow she needs will be  130 inches.

Given,

The side length of pillow is $(2x^2 + 1) \ inches$.

The side length of another pillow is $4x-7 \ inches$.

We know that perimeter of square will be,

$P=4\times length$

So the perimeter of pillow will be,

$P=4\times (2x^2+1)$

$P=8x^{2} +4$

Similarly, the perimeter of another pillow will be,

$P=4\times (4x-7)$]

$P=16x-28$

Hence,the total length of ribbon that she needs for both the pillows will be,

$8x^{2} +4+16x-28\\8x^{2} +16x-24\\4(2x^{2} +4x-6)$

If $x=3.5$ then the total length of ribbon will be,

$4(2\times 3.5^{2}+4\times 3.5-6)\\4(2\times 12.25+14-6)$

$4(24.5+8)$

$4\times 32.5$

$130 \ inches$.

Thus the required expression will be $4(2x^{2} +4x-6)$ and the total length of ribbon she needs will be 130 inches.

So, the correct option will be (D).

For more details on perimeter of square follow the link:

https://brainly.com/question/5402168