Answer:
The side length of the original square was 6 inches
Step-by-step explanation:
we know that
The area of a square is
[tex]A=b^2[/tex]
where
b is the length side of the square
Let
x ---> the length of the original square
The area of the original square is
[tex]A=x^{2}\ in^2[/tex]
The length of the smaller square is
[tex]b=(x-3)\ in[/tex]
The area of the smaller square is
[tex]A=(x-3)^2\ in^2[/tex]
The area of the smaller square is 1/4 the area of the original square
so
[tex](x-3)^2=\frac{1}{4} x^{2}[/tex]
solve for x
[tex]x^2-6x+9=\frac{1}{4} x^{2}[/tex]
Multiply by 4 both sides
[tex]4x^2-24x+36=x^{2}[/tex]
[tex]4x^2-x^2-24x+36=0\\3x^2-24x+36=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
x=2, x=6
see the attached figure
The solution is x=6 in
Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)
therefore
The side length of the original square was 6 inches
