Question

The area of a rectangular deck is x2 + 5xy – 24y2 and the width of the deck is x – 3y. Determine an expression for the length of the deck.

Answer 1

Given:

`\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}`

Area of a rectangle = Length x width.

Thus, Length = area/width

`Length\text{ = }\frac{\text{x}^2+5xy-24y^2}{x-3y}`
`\begin{gathered} Length=(x^2+8xy-3xy-24y^2)/(x-3y) \\ \\ Length=(x(x+8y)-3y(x+8y))/((x-3y)) \\ \\ \end{gathered}`
`\begin{gathered} Length=((x+8y)(x-3y))/((x-3y)) \\ \\ Length=((x+8y)(x-3y))/((x-3y)) \\ \\ Length=x+8y \end{gathered}`

The length = x + 8y