a farmer wishes to enclose a recectangular garden with 300 yard fencing, river runs along one side of the garden no fencing is need there, what are the dimensins of th rectangle if the area is 10450 square yards
a=l*w
10,450=300*W
where did you get 300W?
If there are two short sides (x) and one long side (y), then
2x+y = 300
a = xy = x(300-2x) = 10450
Now solve that for x, the short side.
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's assume that the length of the rectangle is L and the width is W.
Given that the total fencing required is 300 yards, we can deduce that the sum of the lengths of all four sides of the rectangle is equal to 300 yards minus the length of the side along the river.
Since no fencing is needed along the river, we can subtract the length of that side from the total fencing required:
300 yards - L yards = L + 2W (the sum of the lengths of the other three sides)
The area of the rectangle is given as 10,450 square yards, which can be expressed as:
A = L * W
Substituting the value of A into the equation, we have:
L * W = 10,450
Now we have two equations:
300 - L = L + 2W -> 300 = 2L + 2W -> 150 = L + W (Equation 1)
L * W = 10,450 (Equation 2)
We can now solve these equations simultaneously to find the dimensions of the rectangle.
From Equation 1, we have:
L = 150 - W
Substituting this value of L into Equation 2:
(150 - W) * W = 10,450
Expanding the equation:
150W - W^2 = 10,450
Rearranging the equation to form a quadratic equation:
W^2 - 150W + 10,450 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's solve it using the quadratic formula.
Using the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -150, and c = 10,450.
Let's calculate the discriminant: b^2 - 4ac
Discriminant = (-150)^2 - 4(1)(10,450) = 22,500 - 41,800 = -19,300
Since the discriminant is negative, it means that there are no real solutions for W. This implies that there is no rectangle that satisfies the given conditions.
Therefore, it is not possible to find the dimensions of the rectangle with the given information.