Question

What are dimensions of three rectangles that can be created with a perimeter of 24?

Answer 1

The perimeter of a rectangle is given by:

2 × length + 2 × width
2l + 2w 
2(l+w)

We want the perimeter to be 24, so the equation is
$2(l+w) = 24$ , divide both sides by 2
$l+w = 12$

We then think of combination of two numbers that sum gives 12

1 + 11
2 + 10 
3 + 9 
4 + 8
5 + 7
6 + 6 ⇒ This combination will give us a square, not a rectangle
7 + 5 ⇒ This repeat the other combination 5+7

So we can have rectangles with combination of length and width

1 by 11
2 by 10
3 by 9
4 by 8, and
5 by 7