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------------------------------------------------ The area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 meters. The area remains unaffected if the length is decreases by 7 metres and breadth is increased by 5 metres. Find the dimensions of the rectangle.

Let's assume the length of the rectangle is L and the breadth is B. According to the given information, when the length is increased by 7 metres and the breadth is decreased by 3 meters, the area remains the same. This can be expressed as (L + 7)(B - 3) = LB. Similarly, when the length is decreased by 7 metres and the breadth is increased by 5 meters, the area remains the same, which can be expressed as (L - 7)(B + 5) = LB.

Next, we can expand these equations to get:

L * B + 7B - 3L - 21 = LB and L * B - 7B + 5L - 35 = LB

Simplifying these equations, we get 7B - 3L - 21 = 0 and -7B + 5L - 35 = 0. Rearranging these equations, we have 7B = 3L + 21 and 7B = 5L - 35.

Now, we can solve these two equations simultaneously to find the values of L and B. Subtracting the second equation from the first, we get 7B - 7B = 3L - 5L + 21 + 35, which simplifies to -2L = 56. Dividing both sides by -2, we find that L = -28. Substituting this value back into the second equation, we get 7B = 5(-28) - 35, which simplifies to 7B = -140 - 35 = -175. Dividing both sides by 7, we find that B = -25.

However, these negative values do not make sense in the context of the problem. We can ignore these solutions and conclude that the dimensions of the rectangle are not possible given the conditions stated in the problem.

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