Question 1038871
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


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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


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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(x)=(170 + 2x^2)/x}}} where x is the width.