Question

The area (in square inches) of a rectangle is given by the polynomial function a(q)=q^2+7q+12 if the width of the rectangle is (q+3) inches what is the length?

Answer 1

Given:

`\begin{gathered} a(q)=q^2+7q+12inches^2\text{ (Area of rectangle)} \\ \text{width =(q + 3) inches} \end{gathered}`

Required: length?

the formula for the area of a rectangle :

`\text{Area of rectangle = length }*\text{ width}`

let the length of the rectangle be l

`\begin{gathered} q^2\text{ + 7q + 12 = (q + 3) }*\text{ l} \\ l\text{ = }\frac{q^2\text{ + 7q + 12}}{q\text{ + 3}} \end{gathered}`

Using the long division method

`l\text{ = (q + 4) inches}`