SOLUTION: Please help me here: "The perimeter of a rectangular sign is 58cm and its area is 204cm^2. Find the length and width of the sign." If you may, please provide a step by step process

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me here: "The perimeter of a rectangular sign is 58cm and its area is 204cm^2. Find the length and width of the sign." If you may, please provide a step by step process      Log On


   

Question 362589: Please help me here: "The perimeter of a rectangular sign is 58cm and its area is 204cm^2. Find the length and width of the sign." If you may, please provide a step by step process so i can learn how to do it, instead of just getting the answer.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
2L+2W=58 FOR THE PERIMETER.
LW=204 FOR THE AREA.
L=204/W NOW REPLACE L WITH (204/W) IN THE FIRST EQUATION & SOLVE FOR W.
2(204/W)+2W=58
408/W+2W=58
(408+2W*W)/W=58
(408+2W^2)/W=58 CROSS MULTIPLY.
2W^2+408=58*W
2W^2+408=58W
2W^2-58W+408=0
2(W^2-29W+204)=0
(W-17)(W-12)=0
W-17=0
W=17 ANS.
W-12=0
W=12 ANS.
L=204/17=12 ANS.
L=204/12=17 ANS.
PROOF:
12*17=204
204=204