Recall the formula for the perimeter of a rectangle.
P=2l+2w ⇔ P=2(l+w)
We also know that the perimeter of a rectangle is 12 and that each side length has to be an integer.
P=2(l+w) and P=12 [0.3em] ⇕ [0.3em] 2(l+w)=12
Next, we can use the equation for the perimeter to find the value of the width w in terms of the length l.
Now, we know that the pair that satisfies the perimeter equation has a form (l, 6-l). Let's now list all possible combinations of side lengths of a rectangle, given that they are integer values!
l
w=6-l
(l, w)
l+w? = 6
1
6- 1= 5
(1, 5)
âś“
2
6- 2= 4
(2, 4)
âś“
3
6- 3= 3
(3, 3)
âś“
4
6- 4= 2
(4, 2)
âś“
5
6- 5= 1
(5, 1)
âś“
6
6- 6= 0
-
*
Out of all rectangles, there are 3 that have integer side lengths and perimeter equal to 12. Thus, there are 3 possible outcomes of this situation.
