Question

The area (in square inches) of a rectangle is given by the polynomial function A(p) = p2 + 9p + 20. If the length of the rectangle is (p + 5) inches, what is the width?

Answer 1

`Width = p + 4`

Explanation:

Given

`Area = p^2 + 9p + 20`

`Length = p + 5`

Required

Determine the width

The area of a rectangle is:

`Area = Length * Width`

This gives:

`p^2 + 9p + 20= (p+5)* Width`

Expand

`p^2 + 4p + 5p + 20= (p+5)* Width`

Factorize

`p(p + 4) + 5(p + 4)= (p+5)* Width`

`(p + 5) (p + 4)= (p+5)* Width`

Divide both sides by p + 5

`p + 4= Width`

`Width = p + 4`