Asked by Jonathan
If 500 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to two decimal places.
Answers
Answered by
Damon
500 = L + 2 w
so
L = 500 - 2 w
Area = L w = (500 - 2 w)w = 500 w - 2 w^2
where is vertex of that parabola?
2 w^2 - 500 w = - A
w^2 - 250 w = -(1/2) A
w^2 - 250 w + 125^2 = -(1/2) A + 15625
(w-125)^2 = -(1/2)( A - 31250)
so
A = 31250 at vertx
so
L = 500 - 2 w
Area = L w = (500 - 2 w)w = 500 w - 2 w^2
where is vertex of that parabola?
2 w^2 - 500 w = - A
w^2 - 250 w = -(1/2) A
w^2 - 250 w + 125^2 = -(1/2) A + 15625
(w-125)^2 = -(1/2)( A - 31250)
so
A = 31250 at vertx
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