The Area of a Square is the square of the measure of one side of the square.
Hence, given the expression for the area of a square, express the given area as the square of an expression to get the measure of one side.
The given expression is:
[tex]100x^2-160x+64[/tex]Rewrite the expression as:
[tex]\begin{gathered} 10^2x^2-(2\times10\times8)x+8^2 \\ =(10x)^2-(2\times10x\times8)+8^2 \end{gathered}[/tex]Recall the binomial expansion:
[tex](a-b)^2=a^2-2ab+b^2[/tex]Substituting a=10x and b=8, it follows that the expression becomes:
[tex](10x-8)^2[/tex]Since the area of a square is the square of the measure of one side, it follows that the measure of one side from the given expression is 10x-8.