The area of pond will be decreased by 3 square feet if its length is decreased by 2 feet breadth is creased by 1 ft. its area will be increased by 4 square feet if the length is increased by 1 ft. its area will be increased by 4 square feet if length in increased by 1 feet and breadth remains same find the dimension of the pond.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the length of the pond is L feet and the breadth is B feet.
According to the first condition, if the length is decreased by 2 feet and the breadth is increased by 1 foot, the area of the pond will be decreased by 3 square feet. Mathematically, this can be expressed as:
(L - 2) * (B + 1) = L * B - 3 Equation 1
According to the second condition, if the length is increased by 1 foot, and the breadth remains the same, then the area of the pond will be increased by 4 square feet. Mathematically, this can be expressed as:
(L + 1) * B = L * B + 4 Equation 2
Now, let's solve these equations to find the dimensions of the pond.
Firstly, we expand Equation 1 and Equation 2:
L*B - 2*B + L - 2 = L * B - 3 Equation 1
L*B + B = L * B + 4 Equation 2
Next, we can simplify the equations:
-L + 2*B = -1 Equation 1 (simplified)
L = 4 Equation 2 (simplified)
We can substitute the value of L from Equation 2 into Equation 1:
-4 + 2*B = -1
Now, solve for B:
2*B = 4 - 1
2*B = 3
B = 3/2 or 1.5
So, the breadth of the pond is 1.5 feet.
Substitute the value of B back into Equation 2 to find the length:
L * 1.5 = L * 1.5 + 4
L * 1.5 - L * 1.5 = 4
0 = 4
We obtained an inconsistency, meaning our assumptions might be incorrect. Please double-check the given information or provide additional data to solve the problem accurately.
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