The perimeter of a patio is 64 feet. the width of the patio is (x+2) feet and the length of the patio is (x+6) feet. what are the dimensions of the patio?

The perimeter formula for a rectangle is 2(length) + 2(width) = perimeter.
Substituting in the expressions for length, width, and perimeter you get the following equation
2(x + 6) + 2(x + 2) = 64
2x + 12 + 2x + 4 = 64  (Used distributive property to simplify)
4x + 16 = 64   (combined like terms)
4x = 48  (subtracted 16 from both sides of the equation)
x = 12    (divided both sides of the equation by 4)
Width is 12 + 2 or 14 ft and the length is 12 + 6 or 18 ft
Dimensions 18 ft by 14 ft