Answer:
To find the perimeter of the original rectangle, we first need to find the dimensions of the rectangle.
Let's assume the length of the original rectangle is L cm and the breadth is B cm.
According to the given information, if the length is decreased by 4 cm, the new length becomes (L - 4) cm. Similarly, if the breadth is increased by 2 cm, the new breadth becomes (B + 2) cm.
We are told that this new rectangle with dimensions (L - 4) cm and (B + 2) cm is actually a square with the same area as the original rectangle.
The area of a rectangle is given by length multiplied by breadth. So, the area of the original rectangle is L * B square cm.
The area of the new square is equal to the area of the original rectangle. Therefore, we can set up the equation:
(L - 4) * (B + 2) = L * B
Expanding the equation:
LB - 4B + 2L - 8 = LB
Simplifying the equation:
2L - 4B - 8 = 0
2L = 4B + 8
L = 2B + 4
Now that we have an equation relating the length and breadth of the original rectangle, we can find the perimeter.
The perimeter of a rectangle is given by the formula: 2 * (length + breadth).
Substituting the value of L from the equation above, we get:
Perimeter = 2 * [(2B + 4) + B]
Perimeter = 2 * (3B + 4)
Perimeter = 6B + 8
Therefore, the perimeter of the original rectangle is 6B + 8 cm.
Explanation: