A rectangular has a perimeter of 12 m if each side is a whole number of meters what is the possible dimensions for the length and width?

Answer 1

The perimeter of a rectangle is equal to 2 times the sum of the length and the width, which we can write as P = 2 (l + w).

We know the perimeter is 12 therefore

12 = 2 (l + w)

l + w = 12 /2

l + w = 6

So now we need to find pairs of integers (not including 0, for a rectangle can't exist with a dimension of 0) which add up to 6.

The pairs are:

1 & 5, 2 & 4 or 3 & 3.

This gives us 5 possible combinations:

Length = 1 Width = 5

Length = 2 Width = 4

Length = 3 Width = 3

Length = 4 Width = 2

Length = 5 Width = 1