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)
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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) (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 where x is the width.
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