Solution:
Given:
[tex]\begin{gathered} Area\text{ of the rectangular deck = x}^2+5xy-24y^2 \\ Width=\text{ x-3y} \\ We\text{ want to determine the expression for the length} \end{gathered}[/tex]Area of a rectangle = Length x width.
Thus, Length = area/width
[tex]Length\text{ = }\frac{\text{x}^2+5xy-24y^2}{x-3y}[/tex][tex]\begin{gathered} Length=\frac{x^2+8xy-3xy-24y^2}{x-3y} \\ \\ Length=\frac{x(x+8y)-3y(x+8y)}{(x-3y)} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} Length=\frac{(x+8y)(x-3y)}{(x-3y)} \\ \\ Length=\frac{(x+8y)(x-3y)}{(x-3y)} \\ \\ Length=x+8y \end{gathered}[/tex]The length = x + 8y
