Question 246187: Please help me solve this word problem.
The perimeter of a rectangle is 210ft. The length is 15ft. less than twice the width. What is the length and the width?
I have tried dividing 210 by 6, getting 35 for each width, and 70 for each length. Then I added the widths (35+35), to get 70. I subtracted 15 from 70 and got a sum of 55 and divided that by 2 getting(27.5). I then added 15 to both of my lengths (15+70+70), and divided that by 2 getting 77.5. Am I correct that the length is 77.5ft., and the width is 27.5ft.?
Found 3 solutions by stanbon, oberobic, dabanfield:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is 210ft. The length is 15ft. less than twice the width. What is the length and the width?
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Let the width be "w".
Length = "2w-15".
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Perimeter = 2(length + width)
210 = 2(2w-15+w)
105 = 3w-15
3w = 120
w = 40 ft (width)
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length = 2w-15 = 80-15 = 65 ft (length)
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Cheers,
Stan H.
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! Perimeter = 2L + 2W, where L = length and W = width.
We are told
L is 15 less than 2W, so we can interpret this as
L + 15 = 2W ...(the length + 15 = 2W)...or equivalently,
L = 2W -15
.
We are told P = 210.
.
Substituting we have:
.
210 = 2L + 2W
210 = 2(2W-15) + 2W
210 = 4W - 30 + 2W
210 = 6W - 30
240 = 6W
6W = 240
W = 40
.
L = 2W - 15 = 80 - 15 = 65
.
So the dimensions are:
L = 65
W = 40
.
By the way we solved it, we know L is 15 less than 2 times width.
But we can check the perimeter.
2L = 2(65) = 130
2W = 2(40) = 80
2L + 2W = 210
Checks.
Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website! The perimeter is 2*length + 2*width or
P = 2*L +2*W = 210
The Length is 15 less than 2 times the width or L = 2*W-15
Substituting 2*W-15 for L in the first equation above we have:
2*(2*W-15) + 2*W = 210
4*W - 30 + 2*W = 210
6*W = 240
W = ?
Solve for W and then substitute that value in L = 2*W -15 to get the value for L.
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