The perimeter of a rectangle is twice the sum of its length and width. the perimeter is 34 meters and its length is 2 meters more than twice its width. what is its length?

The answer is 12 m.

The perimeter (P) of a rectangle is twice the sum of its length (l) and width (w):
P = 2(l + w)
P = 34
⇒ 2(l + w) = 34
⇒ l + w = 34/2
⇒ l + w = 17

Length is 2 meters more than twice its width: l = 2w + 2

Now we have the system of equations:
l + w = 17
l = 2w + 2

Use the substitution method and substitute l from the second equation into the first equation:
2w + 2 + w = 17
2w + w = 17 - 2
3w = 15
w = 15/3
w = 5

Now, substitute w into the equation:
l = 2w + 2
l = 2 * 5 + 2
l = 10 + 2
l = 12