Given:
[tex]Area=16x^2-40xy+25y^2[/tex]To determine the side of the square, we first note that formula of the area of a square is:
[tex]Area=(Side)^2[/tex]Hence,
[tex]Side=\sqrt{Area}[/tex]Now, we solve for the side of the square:
[tex]\begin{gathered} S\imaginaryI de=\sqrt{Area} \\ S\imaginaryI de=\sqrt{16x^2-40xy+25y^2} \\ Simplify\text{ and rearrange} \\ S\mathrm{i}de=\sqrt{(4x-5y)^2} \\ \end{gathered}[/tex]Then, we apply the radical rule:
[tex]\sqrt[n]{a^n}=a,\text{ assuming a}\ge0[/tex]So,
[tex]\begin{gathered} S\imaginaryI de=\sqrt{(4x-5y)^2} \\ S\mathrm{i}de=4x-5y \end{gathered}[/tex]Therefore, the side of the square is:
[tex]4x-5y[/tex]