gopi has rectangular garden plot surrounded by 200 meter of fence. find the width of the garden if its area is 2400 square meter.
Perimeters=2(L+B)=200
L+B=100
L=(100-B).....(**)
LB=2400.....(***)
Plug (**) into (***)
B(100-B)=2400
-B²+100B=2400
B²-100B+2400=0
Hint -40×-60=2400
-40-60=-100
Note that the length is greater than the width
Now what would B look like?
2L + 2W = 200
Eq1: L + W = 100.
L*W = 2400
L = 2400/W.
2400/W + W = 100
2400 + W^2 = 100W
W^2 - 100W + 2400 = 0
W = (100 +- sqrt(10000-9600))/2 = 60, and 40 Ft.
W = 40 Ft., the shortest length.
In Eq1, replace W with 40 and solve for L.
To find the width of the garden, we need to use the information given in the problem.
Let's assume the length of the garden plot is L and the width of the garden plot is W.
According to the problem, the garden plot is rectangular and is surrounded by 200 meters of fence. This means that the perimeter of the garden plot is 200 meters.
Perimeter = 2(L + W)
Since the garden plot is rectangular, the two lengths (L) will be on opposite sides, and the two widths (W) will also be on opposite sides.
Therefore,
2(L + W) = 200
Now, we are given that the area of the garden is 2400 square meters.
Area = Length * Width
2400 = L * W
Now we have two equations:
2(L + W) = 200
L * W = 2400
We can solve this system of equations using substitution or elimination method to find the values of L and W.
Let's use the substitution method:
From the first equation, we can express L in terms of W:
L = 100 - W/2
Now substitute this value of L in the second equation:
(100 - W/2) * W = 2400
Simplifying this equation:
100W - (W^2)/2 = 2400
Multiplying everything by 2 to eliminate the fraction:
200W - W^2 = 4800
Rearranging the equation:
W^2 - 200W + 4800 = 0
Now we have a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula.
Factoring:
(W - 40)(W - 120) = 0
W = 40 or W = 120
Therefore, there are two possible solutions for the width of the garden: 40 meters or 120 meters.
Hence, the width of the garden could be either 40 meters or 120 meters.