Answer:
Option 1 - [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Step-by-step explanation:
Given : 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.
To find : Which quadratic equation can be used to find s, the side length of the square quilt?
Solution :
The first quilt will be square,
Let the side of square be s
The area of the square is [tex]A=s\times s[/tex]
The second quilt will be a rectangle,
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.
Width of the rectangle = [tex]\frac{1}{2}s[/tex]
Length of the rectangle = s+6
Area of the rectangle is [tex]A=(\frac{1}{2}s) \times (s+6)[/tex]
According to question,
Area of square and rectangle are equal,
So, [tex]s\times s=(\frac{1}{2}s) \times (s+6)[/tex]
[tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Therefore, Option 1 is correct.
The required equation is [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
