Answer: 20 feet by 20 feet.
Step-by-step explanation:
1. You know that [tex]x[/tex] is the original measure of one side. Since it is a square, all its sides are equal.
2. Therefore, to solve the problem you only need to solve for [tex]x[/tex], as you can see below:
- You have that:
[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex]
- Then, you obtain the following quadratic equation:
[tex](x-8)^{2} =144\\x^{2}-2(x)(8)+8^{2}=144\\x^{2}-16x-80=0[/tex]
- Apply the Quadratic formula to solve it:
[tex]x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}\\a=1\\b=-16\\c=-80[/tex]
- Then, you obtain:
[tex]x_1=20\\x_2=-4[/tex]
3. The dimensions cannot be negative, therefore, the answer is: 20 feet by 20 feet.
