SOLUTION: The perimeter of a rectangle is 8x+2 and the width is x+2. Express the area as a trinomial.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The perimeter of a rectangle is 8x+2 and the width is x+2. Express the area as a trinomial.      Log On


   

Question 118606: The perimeter of a rectangle is 8x+2 and the width is x+2. Express the area as a trinomial.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let L=expression for length

So we know that perimeter is

P=2W%2B2L


8x%2B2=2%28x%2B2%29%2B2L Now plug in P=8x%2B2 and W=x%2B2



8x%2B2=2x%2B4%2B2L Distribute


8x%2B2-2x=4%2B2L Subtract 2x from both sides


8x%2B2-2x-4=2L Subtract 4 from both sides


6x-2=2L Combine like terms


3x-1=L Divide both sides by 2 to isolate L


So the length of the rectangle is L=3x-1


Now multiply the length and the width to get the area:


A=%283x-1%29%28x%2B2%29


A=3x%5E2%2B5x-2 Now foil


So the area is A=3x%5E2%2B5x-2