Can you help me with this?

Question

Adam is planning a rectangular patio that will have an area of 16x² + 20x square feet. 

The length of the patio will be 4x feet. 

Is it possible to find the width? If it is possible find the width and explain how you found it; if it is not possible explain your reasoning.

Answer 1

We are given that the area is

A = 16x² + 20x

But, we also know

A = (width)(length)

and length = 4x

By combining our equations and substituting our variable expression for the length we get

16x² + 20x = (width)(4x)

Divide both sides by 4x to get

width = (16x² + 20x)/(4x)

Recall that (A+B)/C = A/C + B/C or more concretely, (1+2)/3 = 1/3 + 2/3

We apply that to get

width = (16x² + 20x)/(4x)

width = (16x²)/(4x) + (20x)/(4x)

width = 4x + 5