Answer:
The new dimensions of the rectangle are breadth = 2 and length = 6. The area of the new rectangle is also 12.
Step by step explanation:
Let the breadth of the rectangle be x. Then, the length of the rectangle is x + 1, since the length is 1 unit more than the breadth.
The area of the original rectangle is:
length x breadth = (x + 1)x = x^2 + x
If the breadth is decreased by 1 unit and the length is increased by 2 units, the new dimensions of the rectangle are:
Breadth = x - 1
Length = x + 1 + 2 = x + 3
The area of the new rectangle is:
length x breadth = (x + 3)(x - 1) = x^2 + 2x - 3
Since both rectangles have the same area, we can set their area expressions equal to each other:
x^2 + x = x^2 + 2x - 3
Simplifying the equation, we get:
x = 3
Therefore, the breadth of the original rectangle is 3, and the length is 4. The area of the original rectangle is 3 x 4 = 12.
The new dimensions of the rectangle are breadth = 2 and length = 6. The area of the new rectangle is also 12.