posted by Marysvoice on .
Building a rectangular room with fixed perimeter of 280ft
what dimentions would yield the maximum area?
What dimentions would yeild the minimum area?
A rectangle of largest area is a square.
So divide your perimeter by 4.
To build a room of minimum area is a rather silly question.
I apologize for my silly question. I followed your advice, revised my question and found my answer. Thank you.
x = length
y = width
A = x y
A = x(140-x)
A = 140 x - x^2
look at shape of parabola by completing the square
x^2 -140 x = -A
x^2 - 140 x + 4900 = -A + 4900
(x-70)^2 = -A + 4900
the vertex will be at x = 70 and A = 4900 and the -A means that the parabola opens down (sheds water) so that vertex is the maximum where x = y =70 as Reiny told you.
since a negative x or y does not make much sense, the area may not get any smaller than zero when x --> 0 or y -->0 0