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9. A rectangle has a length that is 1 unit more than its breadth. If the breadth is decreased by 1 unit and the length is increased by 2 units, both rectangles have the same area. What are the dimensions of these rectangles?​

User Cherryann
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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.
User Jeff Keslinke
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