Set up a system of equations where W is width, and L is length.
Set up the first equation for the perimeter
W + W + L + L = 99
Simplify
2W + 2L = 99
Set up another equation for the width and length ratio
2W = L
Subtract L from both sides of the second equation
2W - L = 0
Subtract the second equation from the first one
(2W + 2L) - (2W - L) = (99) - (0)
Distribute the -1
2W + 2L - 2W + L = 99 - 0
Simplify by combining like terms
3L = 99
Divide both sides by 3
L = 33
Plug 33 in for L in the original second equation
2W = 33
Divide both sides by 2
W = 33/2
Therefore, the rectangle's dimensions are 33x16.5