dont know
2007-07-24 12:23:50 · 6 answers · asked by Lisa H 1 in Science & Mathematics ➔ Mathematics
its whose
2007-07-24 12:25:00 · update #1
Reedrock's answer is pretty good except that 7*8 is 56.
P=2(L+W)
A= LW
So if there is a rectangle, that means that the sides opposite each other are the exact same length, which is why we can multiply the sum of the length and width by 2. Next, you can divide the perimeter by 2 to find the sum of the sum of the length and width.
The numbers closest to each other make the biggest area. The easiest way to find the numbers closest to each other is to divide the sum of the length and width by 2. In this problem you will get 7.5. This will be measure for both the length and width. Then to get the area, you multiply the length by the width and get 56.25, which is slightly bigger than 7*8.
This is a square, but remember that all squares are rectangles, but not all rectangles are squares.
If you need whole numbers and you have a decimal, then round up for one and down for the other.
2007-07-24 12:49:22 · answer #1 · answered by girl person 2 · 0⤊ 0⤋
W = width
L = length
2 (W + L) = 30
W + L = 15
What is the maximum (W x L) assuming you can only use whole numbers
1 x 15 = 15
2 x 13 = 26
3 x 12 = 36
4 x 11 = 44
5 x 10 = 50
6 x 9 = 54
7 x 8 = 48
That would be 54. So it would be 6 x9.
There is probably a formula that will give you the exact number in decimals..... Anyone?
2007-07-24 19:33:44 · answer #2 · answered by KenCosgrove 2 · 0⤊ 1⤋
It's a square 7.5 ft on a side. Proving it requires a little calculus, or at least this much algebra:
P = 2L + 2W = 30
L + W = 15
W = 15 - L
A = LW = L(15-L) = -L² + 15L
now in alg 1 you know that's a parabola that opens downward, intersecting the L axis at 0 and 15, and you know the vertex (and highest point) is on the line of symmetry, halfway between the intercepts, which makes L = 7.5 and W = 15 - 7.5 = 7.5.
In calculus you'd find the derivative of A(L), which would be dA/dL = -2L + 15, and set it equal to 0, so 2L = 15, L = 7.5.
2007-07-24 19:35:11 · answer #3 · answered by Philo 7 · 1⤊ 0⤋
Philo is correct. i.e. a rectangle has a perimeter equal to 2*(a+b), therefore in your case a+b=15. The largest product of a*b is indeed when a=b=7.5.
However, if you are being picky and not including the possibility of square, then you might say a=7.5 plus a very very very small amount, and b=15-a etc
:)
2007-07-24 19:52:56 · answer #4 · answered by amg_nz 1 · 0⤊ 0⤋
10 by 5 gives you 50ft^2
2007-07-24 19:31:27 · answer #5 · answered by Justin M 4 · 0⤊ 0⤋
2a+2b=30 or a=15-b
A=ab=b(15-b)
solve dA/db=0 for b
15-2b=0=> b=7.5
a=7.5
it will be a square
area=56.25 sqft
2007-07-24 19:37:30 · answer #6 · answered by Alberd 4 · 0⤊ 0⤋