SOLUTION: Billy has 52 m of fencing. He wishes to maximize the area of a rectangular garden. What are the dimensions of the rectangle he should use to maximize the area? What is the maximum

Question 257085: Billy has 52 m of fencing. He wishes to maximize the area of a rectangular garden. What are the dimensions of the rectangle he should use to maximize the area?
What is the maximum area?
If one side of the rectangular garden is a house and therefore will not require fancing, what dimensions should b used to maximize the area?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We have two formulas:
(i)
(ii)
From the given information, (i) becomes
(iii)
or
(iv)
Solving (iv) for L, we get
(v)
substituting (v) into (ii) we get
(vi)
or
(vii)
applying the quadratic, we get

so, the dimensions are 13 x 13 and the area is 169 sq. m.
--
If one side is a house, then
(i)
(ii)
From the given information, (i) becomes
(iii)
Solving (iii) for L, we get
(iv)
substituting (iv) into (ii) we get
(v)
or
(vii)
applying the quadratic, we get

so, the dimensions are 26 x 13 and the area is 338 sq. m.
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