find the side lengths of the largest garden wut is its area
2007-09-18 14:06:31 · 12 answers · asked by Shannon M 1 in Science & Mathematics ➔ Mathematics
Hi,
The largest area is always a square, so it is 7 by 7 for 49 square feet of area.
You can prove that by letting one side have a length of x. Since one length and one width will use up half the perimeter, then the other side is 14 - x. The area could be found by the formula A = LW or y = x(14 - x) or y = 14x - x². This is the graph of a parabola that opens down and has a maximum area at its vertex, which is on the axis of symmetry. The axis is found by the formula x = -b/(2a) where a is the number in front of x² and b is the number in front of x. So the axis is x = -14/(2*-1) = -14/-2 = 7. That show that each side of the rectangle will be 7, since 14 - x would also be 7.
I hope that helps!! :-)
2007-09-18 14:13:04 · answer #1 · answered by Pi R Squared 7 · 1⤊ 1⤋
Maximum area exist when side length times end length is maximum and the distance around the rectangle is 28 yards. Start with a side length of 13 and a end length of 1 and calculate the area. In increments of one increase the end length by 1 while decreasing the side length by 1 until the side becomes 1 and the end length becomes13. Calculate the area after each incremental change. The maximum area will occur when the side length is 7 and the end length is 7. The maximum area will be 49 square yards.
2007-09-26 20:20:13 · answer #2 · answered by PILL 1 · 0⤊ 0⤋
length and width are both 7
area = 7 x 7 = 49 square yards
btw the largest area always comes from having a square. So if all 4 sides were equal then divide 28 by 4.
2007-09-18 21:12:38 · answer #3 · answered by sfroggy5 6 · 0⤊ 0⤋
A square has the largest possible area out of all type of rectangles having the same perimeter
The perimeter here is 28 yards
Hence each side of the square is 28/4=7 yards
Therefore,the area is 49 yds^2
2007-09-18 21:16:46 · answer #4 · answered by alpha 7 · 0⤊ 1⤋
Let x = sides
Find the sides:
2(2x) = 28
4x = 28
x = 7
Area:
= 7 * 7
= 49
Answer: each side is 7 yards, area is 49 square yards
Proof (perimeter is 28 yards):
= 2 * (7 + 7)
= 2 * 14
= 28
2007-09-18 21:15:10 · answer #5 · answered by Jun Agruda 7 · 3⤊ 1⤋
given
Perimeter = 28 yards
P = 28 = 2(l + w) , where l and w are lenght and width
l + w = 28/2 = 14
l = 14 - w
area = l*w
A = (14-w)w
= 14w - w^2
area will be maximum, when dA/dw = 0
dA/dw = 14 - 2w =0
2w = 14
w = 7
l = 7
When it is in the form of a square the area will be maximum
2007-09-18 21:18:40 · answer #6 · answered by mohanrao d 7 · 0⤊ 1⤋
28=2l+2w Divide by 4, the sum of the leading coefficients.
28/4= 7
7=l+w
Solve the rest.
2007-09-26 21:09:23 · answer #7 · answered by Anonymous · 0⤊ 0⤋
7 yards by 7 yards of fencing
2007-09-26 19:02:20 · answer #8 · answered by kalleygurl 2 · 0⤊ 0⤋
Let sides be x and y
2x + 2y = 18
x + y = 14
y = 14 - x
A(x) = x (14 - x)
A (x) = 14x - x²
A `(x) = 14 - 2x = 0 for max. vale of A(x)
x = 7
Side are each 7 yards for max. area (a square)
2007-09-19 14:15:12 · answer #9 · answered by Como 7 · 2⤊ 0⤋
7 yards on each side... a square is a rectangle
7x7=49
2007-09-18 21:13:30 · answer #10 · answered by Love always, Kortnei 6 · 0⤊ 0⤋