Question

JD is repainting some of the walls in the classrooms at Golder. One wall had a width that is 4 feet less than it's length. The wall has an area of 140 square feet. What is the length of the wall.

Answer 1

Let the length of the wall be l.

The width is 4ft less than its length.

Therefore, the width is l - 4.

The wall is rectangular, therefore

`\text{ area of wall = length}*\text{ width}`

Hence,

`\begin{gathered} l(l-4)=140 \\ l^2-4l=140 \\ \Rightarrow l^2-4l-140=0 \\ l^2+10l-14l-140=0 \\ \Rightarrow l(l+10)-14(l+10)=0 \\ \Rightarrow(l-14)(l+10)=0 \\ \Rightarrow l-14=0,l+10=0 \\ \Rightarrow l=14,l=-10 \\ \text{ Since l cannot be negative, then the only possibility is} \\ l=14\text{ ft} \\ \end{gathered}`

Hence, the length of the wall is 14 feet