Question 836332
A = LW ... area of rectangle


90 = LW


LW = 90


L = 90/W


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P = 2L + 2W


46 = 2L + 2W


46 = 2(90/W) + 2W


46 = 180/W + 2W


W*(46) = W(180/W + 2W) ... Multiply both sides by W so we can clear out that fraction.


W*(46) = W(180/W) + W(2W)


46W = 180 + 2W^2


0 = 180 + 2W^2 - 46W


2W^2 - 46W + 180 = 0


2(W^2 - 23W + 90) = 0


W^2 - 23W + 90 = 0/2


W^2 - 23W + 90 = 0


(W - 18)(W - 5) = 0


W - 18 = 0 or W - 5 = 0


W = 18 or W = 5


if the width is W = 18, then the length is L = 90/W = 90/18 = 5.


if the width is W = 5, then the length is L = 90/W = 90/5 = 18.



So regardless of which value you pick for W, the other value for L will be the other solution.


In essence, the dimensions are <font color="red">18 meters by 5 meters</font>



Check: 


A = LW = 18*5 = 90 square meters ... area checks out


P = 2L + 2W = 2*18 + 2*5 = 36+10 = 46 meters ... perimeter checks out