A)
The area of a square is equal to the square of the length of its side. Since the side of the square is x, then the area is equal to x^2. Since the area must be equal to 400 square inches, then:
[tex]x^2=400[/tex]
B)
To solve this equation, take the square root to both members of the equation:
[tex]\Rightarrow\sqrt[]{x^2}=\sqrt[]{400}[/tex]
The square root of the square of a variable is always equal to the absolute value of that variable. The square root of 400 is 20. Then:
[tex]\Rightarrow|x|=20[/tex]
This equation has two solutions:
[tex]\begin{gathered} x_1=20 \\ x_2=-20 \end{gathered}[/tex]
C)
Since x represents a distance, the negative solution does not make sense in the context of the problem.
D)
Since a square has four sides of equal lengths, and one side has a length of 20 inches, then four times 20 inches is the length needed to go around the painting. Since 4*20=80, then, the length of the wood trim needed to go around the painting, is:
[tex]80\text{ inches}[/tex]
