Question

A rectangle has an area given by A=x^2-3x-10. Find possible expressions for the length and width of the rectangle.

Answer 1

`A=x^2-3x-10`

A negative Area wouldnt' make any sense, therefore:

`\begin{gathered} x^2-3x-10\ge0 \\ \text{Factor:} \\ (x-5)\cdot(x+2)\ge0 \\ \text{The area is given by:} \\ A=w\cdot l \\ \text{Let:} \\ w=\text{width}=(x-5) \\ l=length=(x+2) \\ \text{The solutions are:} \\ x\ge5 \\ or \\ x\le-2 \end{gathered}`

Since a negative measure wouldn't make any sense:

`x\ge5`

Therefore:

`\begin{gathered} w\ge5 \\ or \\ l\ge5 \end{gathered}`