You have a rectangular yard that has perimeter of 72 meters. The current area is between 300 and 350. What are the dimensions of your current fenced in space
you want two partitions of 36 that multiply to between 300 and 350
18x18 = 324
17x19 = 323
16x20 = 320
15x21 = 315
14x22 = 308
Currently you have a rectangular yard that has a perimeter of 72 meters.the current area is between 300 and 350
11 times 14
To find the dimensions of the current fenced-in space, we need to set up a system of equations based on the given information.
Let's assume the length of the rectangular yard is L meters, and the width is W meters.
We know that the perimeter of a rectangle is given by the formula: Perimeter = 2(L + W).
From the given information, we have:
Perimeter = 72 meters
2(L + W) = 72
We also know that the area of a rectangle is given by the formula: Area = L * W.
From the given information, we have:
Area = between 300 and 350 square meters
300 <= L * W <= 350
Now we have a system of equations to solve. We can do this by substitution or elimination method. Let's use substitution method:
From the perimeter equation, we can solve for L:
L = (72 - 2W) / 2
L = 36 - W
Substituting this value of L into the area equation:
300 <= (36 - W) * W <= 350
Expanding the equation:
300 <= 36W - W^2 <= 350
Rearranging the equation to form a quadratic equation:
W^2 - 36W + 300 >= 0
W^2 - 36W - 300 <= 0
Now, we can solve this quadratic equation to find the range of possible values for W. Once we find the values of W, we can substitute them back into the equation L = 36 - W to get the corresponding values of L.
Using the quadratic formula:
W = (36 ± sqrt((-36)^2 - 4(1)(-300))) / 2(1)
W = (36 ± sqrt(1296 + 1200)) / 2
W = (36 ± sqrt(2496)) / 2
W = (36 ± 49.96) / 2
So, the values of W are:
W1 = (36 + 49.96) / 2 = 42.98 (approximately)
W2 = (36 - 49.96) / 2 = -6.98 (approximately)
Since width cannot be negative, we discard the second solution.
Now, substitute W = 42.98 into the equation L = 36 - W:
L = 36 - 42.98
L ≈ - 6.98
Again, length cannot be negative, so we discard this solution as well.
Therefore, there are no valid dimensions for the current fenced-in space given the constraints of the perimeter and area.