A rectangular balcony has an area of 12 square feet and a perimeter of 16 feet. What are the dimensions of the balcony?

Let the length be ( l ) and the width be ( w ). We know that ( lw = 12 ) (area) and ( 2l + 2w = 16 ) (perimeter), which simplifies to ( l + w = 8 ). Solving these equations simultaneously, we can express ( w ) as ( 8 - l ) and substitute into the area equation: ( l(8 - l) = 12 ). This leads to the quadratic equation ( l^2 - 8l + 12 = 0 ), which factors to ( (l - 6)(l - 2) = 0 ). Thus, the dimensions are ( l = 6 ) feet and ( w = 2 ) feet, or vice versa.