math help? i forgot how to do this...?

Question

we're still doing this review thing and, once again, i have forgotten something i learned years ago. (i always seem to forget the simplest things)
ok. so how do i find the maximum area for a given perimeter of a rectangle? i need to state the length and width of the rectangle. i need to do it for the following:

- 25 mm
-18 yards
-42 cm

but if you could breifly/simply walk me through it to refresh my memory, that'd be great too.

Answer 1

try to make square.
6+8=14 6x8=48
7+7=14 7x7=49

Answer 2

The way to do this is to write an equation that represents the area of the rectangle, and then maximize it.

Let P be a constant, representing the total amount of perimeter material. Units are irrelevant.
Let w be a variable, representing the width of the rectangle.
Thus, the length must be equal to half of the remaining material after both width sides have been constructed, i.e:
length = (P-2w)/2

Since area = length * width:
A = w * (P-2w)/2
A = w * (P/2 - w)
A = w * P/2 - w^2

Now this equation has to be maximized. If you don't know calculus, you can use a graphing calculator to approximate the maximum. However, if you have seen derivatives before:
A' = P/2 - 2w
We set this equal to zero, since we want to find the value of w for which the function has a local maximum, a point with slope of zero.
0 = P/2 - 2w
w = P/4
There you have it. The width for a rectangle of maximum area is simply equal to the total amount of perimeter material divided by four -- also known as a square. This should not be a surprising result. For every unit of length you add to the width of the square, as you deform it to a rectangle, you have to remove one unit from the length. Thus, it makes some sense that the maximum area will be achieved when both length and width are the same value.

Answer 3

The rectangle is constructed of 4 sides 25 mm.

The perimeter = 2 (L+w) = 25

You could then divide the rectangle by 2, The rectangle can always be divided in two right triangles and then you could use the laws of Triangles to figure our the rest.

Answer 4

Perimeter = 2(width) + 2 (length)
Area = width x length
From the first equation, width = (perimeter/2) - length
Therefore, area = [(perimeter/2) - length] x length
You can then graph this quadratic equation and find the maximum value. The y-value at this point will be the area, and the x-value will be the length.

Answer 5

The basic answer is going to be that you maximize area with a square. So, if the perimeter is 25, then the length and width are one quarter of the perimeter, or 12.5.

See http://www.analyzemath.com/calculus/Problems/optimize_area.html

Answer 6

What numbers equal to the perimeter? LIke 5 times 5 =25, right? its kinda like that. i hope that works out 4 you.

Answer 7

once you've a chum who's prepared to address the questions for you, then ask that individual. I doubt every person would favor to address the homework for you-- even with if it were an wide chum because of ways time eating it really is. yet another selection you've is to flow to a chum's living house in the course of the weekend and do the homework with them, or use their mathbook in the journey that they were complete. Your very last selection will be now to not do it, and face your instructor's wrath Monday morning.