Answer:
4
Step-by-step explanation:
Consecutive even integers mean the numbers are (for example) 2, 4, 6 or 214, 216, 218, ec.
This means the sides will be (if x is an even integer, which we shall assume it is):
x, x + 2, x + 4, x + 6
(four sides, four expressions)
We can set this up into an equation by writing it more like this:
(x) + (x + 2) + (x + 4) + (x + 6)
The shortest side (x) is 24 units shorter than the perimeter. We can use this by writing it like this:
(x) + (x + 2) + (x + 4) + (x + 6) = x + 24
I say this because x is 24 units less, so then adding it will result in the perimeter.
Now we can finally solve!
(our equation) (x) + (x + 2) + (x + 4) + (x + 6) = x + 24
(simplfy) 4x + 2 + 4 + 6 = x + 24
(simplfy) 4x + 12 = x + 24
(subtract 12 & x from both sides) 3x = 12
(divide both sides by 3) x = 4
(check) 4 + 6 + 8 + 10 = 28
(check) 28 - 4 = 24
(answer) Shortest side (x) is 4!
I hope this is correct + makes sense, have a nice day and good luck! :D
