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

Answer:

$Width = p + 4$

Step-by-step 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

$p + 4= Width$

$Width = p + 4$