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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 :

MRROYALGO

Answer:

[tex]Width = p + 4[/tex]

Step-by-step explanation:

Given

[tex]Area = p^2 + 9p + 20[/tex]

[tex]Length = p + 5[/tex]

Required

Determine the width

The area of a rectangle is:

[tex]Area = Length * Width[/tex]

This gives:

[tex]p^2 + 9p + 20= (p+5)* Width[/tex]

Expand

[tex]p^2 + 4p + 5p + 20= (p+5)* Width[/tex]

Factorize

[tex]p(p + 4) + 5(p + 4)= (p+5)* Width[/tex]

[tex](p + 5) (p + 4)= (p+5)* Width[/tex]

Divide both sides by p + 5

[tex]p + 4= Width[/tex]

[tex]Width = p + 4[/tex]

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