Final answer:
To determine the side length s of the square quilt, we create a quadratic equation by setting the area of the square quilt s^2 equal to the area of the rectangular quilt (s/2)(s + 6). Solving this quadratic equation gives us s = 6.
Step-by-step explanation:
To solve for the side length s of the square quilt, we must set up an equation for the area of both quilts. For the square quilt, the area is s^2. The second quilt is a rectangle with width s/2 and length s + 6, so its area is given by (s/2)(s + 6). Aisha wants the two quilts to have the same area, so we set the two expressions equal to each other:
s^2 = (s/2)(s + 6)
To find s, we must solve this quadratic equation. First, we distribute the right side to get:
s^2 = s^2/2 + 3s
Multiplying each term by 2 to eliminate the fraction, we get:
2s^2 = s^2 + 6s
Subtracting s^2 from both sides leads to:
s^2 = 6s
Finally, we can divide each side by s (assuming s is not zero) to get:
s = 6
Therefore, the quadratic equation that can be used to find s, the side length of the square quilt, is s^2 = 6s.