SOLUTION: In rectangle ABCD, AB=(x-5y+94), BC= 3x+2y-82), CD= (4x-6y+55), and DA= (5x+4y-164). Find the perimeter of the rectangle. Could you please help me on this problem?

Question 286991: In rectangle ABCD, AB=(x-5y+94), BC= 3x+2y-82), CD= (4x-6y+55), and DA= (5x+4y-164). Find the perimeter of the rectangle.
Could you please help me on this problem?

Found 2 solutions by richwmiller, scott8148:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
opposite sides of a rectangle are equal
set the opposite sides equal
You will have two equations with two unknowns x and y
after you find x and y then you have to calculate each side and add them up.
that is the perimeter.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the opposite sides of a parallelogram (rectangle) are equal
___ this leaves you with a system of equations in x and y

x - 5y + 94 = 4x - 6y + 55 ___ 3x - y = 39

3x + 2y - 82 = 5x + 4y - 164 ___ 2x + 2y = 82 ___ x + y = 41 ___ y = 41 - x

substituting ___ 3x - (41 - x) = 39 ___ 4x = 80 ___ x = 20

substituting ___ y = 41 - (20) = 21

plug in the values for x and y to find the perimeter (sum of the sides)
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