Your missing some info here before we can help, is the longer piece 3 feet larger than twice the shorter piece or 3 feet smaller than twice the shorter piece?
If the question is greater than, than y = length of longer piece, and x = length of the shorter piece.
we know that the longer length is 3 feet longer than twice the shorter length, so we can make the equation: Longer length y = 3 + 2x This is saying take twice the shorter and add 3.
We also know that both lengths have to add up to 12. So x+y=12. Since you know that y= 3 + 2x, you can plug that into the other equation for y.
so instead of x+y=12, you get x + (3 + 2X) = 12. Since its all addition you can remove the ( ). and have x+3+2x = 12. Combine the x+ 2x = 3x, so the equation is now 3 + 3X = 12. Now solve for x.
Subtract 3 from both sides, to get 3x=12-3, or 3x=9. Now divide by 3 to get x=3. So we know the shorter is now 3 feet. Now plug that into the other equation x+y=12, so 3+y=12, and you can see that y=9.
