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can someone help me with this question? I think I know what to do but might be on the wrong path.?

john has 24m of fencing to make a rectangular flower garden. He plans to use his house as one side of the garden. What dimensions will give the maximum "area"?

Public Comments

1. A = x^2 = (24/3)^2 = 8^2 = 64m^2
2. the area is a*b the length is a + 2b = 24 ( since one side is the house ). so you have to maximize the function Area(a,b) = a*b substitute the connstraint a = 24 - 2b and you will get Area(b) = (24-2b)*b the function is a parabole with its max in the top, graph the function and you know the answer. the zeros are b=0, b = 12, thus the top is on b = 6 and then a = 24-2*6 = 12 ant the area 6*12 = 72