Question

how many rectangles of a perimetre of 10 can be drawn

Answer 1

perimeter = 2(l+b)

so

2(l+b)=10

(l+b)=5
Since length and width are positive integers in centimeters. Therefore, possible dimensions are

(2, 3). (1,4). (3,2) (4,1)

Answer 2

Solution:-

Actually there can be infinite number of rectangles. Lemme explain,

perimeter = 2(L +B) = 10

⇒L +B = 5

now, we can take any positive number, can be fraction also.

It should be noted that L or B cannot be Zero, because if it is zero, then rectangle could not be formed.

If it is asked, the length and breadth can only be a natural number, then possible dimensions

are (length,breadth) as (2,3), (1,4), (3,2), (4,1)
then only 4 rectangles are possible.

Otherwise, infinite number of rectangles are possible.

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@GauravSaxena01