W is the width of the quilt, the restrictions are given by the inequality:
7.7ft ≤ W ≤ 8.9 ft
Remember that for a rectangle of length L and width W, the area is:
A = L*W
In this case, we know that:
L = 1.2*W
Replacing that we get:
A = 1.2*W²
And we know that the area must be between 72 square feet and 96 square feet, then:
72ft² ≤ 1.2W² ≤ 96ft²
Now we can divide all by 1.2:
(72ft²)/1.2 ≤ W² ≤ (96ft²)/1.2
60ft² ≤ W² ≤ 80ft²
If we apply the square root in the 3 sides of the inequality, we get:
√60ft² ≤ √W² ≤ √80ft²
7.7ft ≤ W ≤ 8.9 ft
These are the restrictions on the width such that the quilt will meet the required area.
If you want to learn more about inequalities:
https://brainly.com/question/18881247
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