Question

The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?

Answer 1

As given by the question

There are given that area of rectangle and width of a rectangle

`\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}`

Now,

From the formula of area of a rectangle:

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

Then,

Put the value of an area and width into the above formula

So,

`\begin{gathered} \text{Area}=\text{length}* width \\ b^2+9b+18=length*(b+3) \end{gathered}`

Then,

`\begin{gathered} b^2+9b+18=length*(b+3) \\ (b+3)(b+6)=\text{length}*(b+3) \\ \text{length}=((b+3)(b+6))/((b+3)) \\ \text{length}=(b+6) \end{gathered}`

Hence, the value of length is ( b + 6 ).