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Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.

Which quadratic equation can be used to find s, the side length of the square quilt?

User Joe Antony
by
7.7k points

2 Answers

6 votes

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.

User Iurii Budnikov
by
8.9k points
3 votes

Answer:

its A

Step-by-step explanation:

I just took the quiz on ed and got it right

User Thodg
by
7.8k points
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