Question

The length of a rectangle is 5 meters longer than its width.The area of the rectangle is 84 m^2.What is the width of the rectangle?

Answer 1

we have that the measures of the rectangle are the following:

`\begin{gathered} l=5+w \\ w=\text{width} \end{gathered}`

then the area is:

`A=l\cdot w=(5+2)w=5w+w^2`

since the area is 84m^2, we have the following equation:

`\begin{gathered} 84=5w+w^2 \\ \Rightarrow w^2+5w-84=0 \\ \Rightarrow(w+12)(w-7)=0 \end{gathered}`

we have that the solutions of the equations are w = -12 and w = 7. We choose w = 7 since the measures of the rectangle must be positive. Therefore, the width of the rectangle is 7 m