SOLUTION: Thanks in advance. Please answer my question please :) the area of a rectangle is 85cm². Express the perimeter of the rectangle as a function of width (x)

Algebra ->  Rectangles -> SOLUTION: Thanks in advance. Please answer my question please :) the area of a rectangle is 85cm². Express the perimeter of the rectangle as a function of width (x)      Log On


   

Question 1038871: Thanks in advance. Please answer my question please :)
the area of a rectangle is 85cm². Express the perimeter of the rectangle as a function of width (x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's set up our length and width variables

L = length
W = width

The area of any rectangle is

area = length*width
A = L*W

Since we're told that the width is x, this means W = x

A = L*W
A = L*x

Now divide both sides by x to isolate L

A = L*x
A/x = L*x/x
L = A/x

-------------------------------------
The width and length are
W = x
L = A/x

but we know that the area is 85 square cm, so A = 85

so,
W = x
L = 85/x

--------------------------------------
We use these two expressions to find the perimeter P

P = 2*L + 2*W
P = 2*(85/x) + 2*x
P = 170/x + 2x
P = 170/x + (2x^2)/x
P = (170 + 2x^2)/x

So the perimeter is P%28x%29=%28170+%2B+2x%5E2%29%2Fx where x is the width.