Question 353686: the perimeter of a rectangle is 160 m. the length is 8m more than twice the width. find the dimensions Found 2 solutions by checkley77, jsmallt9:Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! L=W+8
2L+2W=160
2(W+8)+2W=160
2W+16+2W=160
4W=160-16
4W=144
W=144/4
W=36 ANS. FOR THE WIDTH.
L=36+8=44 ANS. FOR THE LENGTH.
PROOF:
2*44+2*36=160
88+72=160
160=160
You can put this solution on YOUR website! Let L = length and W = width.
"The length is 8m more than twice the width" translates into:
L = 8 + 2W
From the information on the perimeter we also know that
160 = 2L + 2W
We can solve this system in several ways. Since the first equation is already soved for L, I will use the Substitution Method and substitute for L in the second equation:
160 = 2(8 + 2W) + 2W
Simplify:
160 = 16 + 4W + 2W
160 = 16 + 6W
Subtract 16 from each side:
144 = 6W
Divide both sides by 6:
24 = W
With L = 8 + 2W we can find L:
L = 8 + 2(24)
L = 8 + 48
L = 56
To check you can make sure that with a length of 56 and a width of 24 the...
- the perimeter is 160, and
- the length is 8 more that twice the width.
This answer checks.
(