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?

Question

asked Sep 23, 2023 234k views

1 Answer

Samuel Huylebroeck · Answer 1 · 2023-09-30T10:55:30+0000

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

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