Pure Maths Question
Please help me to solve the following question:
Show that a rectangle with a given perimeter achieves maximum area only if it is a square.
- 8 years agoFavorite Answer
假設矩形的周長是 A, 令此矩形的其中一邊長是X,則另一邊長必為(A/2-X)
- 8 years ago
- DaSaGwaLv 78 years ago
Terry +1! Nice job! you didn't use "derivative" but "completing the square" (algebraic method).
2012-11-01 07:47:19 補充：
assume x and y are the two side of the rectangular, hence
2x + 2y = A (A is fixed perimeter)
==> x = 1/2(A- 2y)
2012-11-01 07:50:30 補充：
area of rectangular = xy = 1/2(A-2y)y = Ay/2 -y^2
for area to be the maximum, d(area)/dy = 0
hence, A/2 − 2y = 0 ==> y = A/4, so x=y=A/4, a square !
2012-11-03 08:55:51 補充：
Using what method to solve a problem depends upon the level of schooling. If a person can understand the meaning of derivatives, then why not uses a more advance way to solve a problem.
2012-11-03 08:57:34 補充：
However, I feel, no matter what level of schooling you are in, a person shall always know a lower level method. After all, it is a foundation for more advanced method.