# The area and perimeter of a rectangle are equal. What are the values of the length and breadth?

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### 2 Answers

The area and perimeter of a rectangle are equal. If the length is l and the breadth is b.

2(l + b) = l*b

This is possible if l + b = (l*b)/2

The above equation can have infinite solutions, for example

l = 4 => b = 4

l = 8 => b = 8/3

l = 16 => b = 16/7

**As there is only equation relating the two variables l and b, there are an infinite number of solutions.**

Let the length of rectangle be l and breadth be b

The given condition can be expressed in equation as following

: 2(l+b) = lb

=> lb-2l-2b=0

=> (l-2)(b-2)-4=0

=> (l-2)(b-2)=4

Because length and breadth are not necessarily integers, there would be an infinite number of solution for (l-2, b-2) which sastisfies the equation above. Therefore, number of solution (l,b) should be in infinite number.