SOLUTION: the perimeter of a rectangle is twice the sum of it's length and it's width. the perimeter is 28 meters and it's length is 2 meters more than twice it's width. what is the length?

Algebra ->  Linear-equations -> SOLUTION: the perimeter of a rectangle is twice the sum of it's length and it's width. the perimeter is 28 meters and it's length is 2 meters more than twice it's width. what is the length?      Log On


   

Question 288222: the perimeter of a rectangle is twice the sum of it's length and it's width. the perimeter is 28 meters and it's length is 2 meters more than twice it's width. what is the length?
Answer by jaydducote(11) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter is (=) twice (two times) the sum of its length and width (L+W).
P=2(L+W)
The perimeter is (=) 28 meters and its length is 2 meters more (+2) than twice (times 2) its width. What is the length?
P=28
L=2+2W
So you know that P=28. Plug that into the first equation:
P=2(L+W)
P=28
28=2(L+W)
then simplify by distributing
28=2L+2W
You also know that L=2+2W, so substitute that for L
28=2(2+2W)+2W
now distribute again
28=4+4W+2W
combine like terms
28=4+6W
subtract 4 from both sides
24=6W
divide by 6 on both sides
4=W
so we know that W=4, but the problem asks for the length, so plug 4 in for W in the equation for length at the top.
L=2+2(4)
L=2+8
L=10
Your answer is that the length of the rectangle is 10 meters (don't forget the unit is meters)