SOLUTION: The perimeter of a rectangle in 42m. The length of the rectangle is3m less than twice the width. Find the length and width of the rectangle.

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Question 621512: The perimeter of a rectangle in 42m. The length of the rectangle is3m less than twice the width. Find the length and width of the rectangle.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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Find the length and width of the rectangle.
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STEP I: Choose variables.
Let L be the length of the rectangle.
Let W be the width of the rectangle.
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STEP II: Write two equations using the information in the problem to model the situation.
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Perimeter (42m) means the distance around the outside of the rectangle. Going around, we have two lengths plus two widths. An equation for this is,
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42=2L%2B2W
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In algebra, the phrase "length is 3 less than twice the width," can be written as,
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L=2W-3
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STEP III: Solve the system of equations to find L and W.
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We'll use the substitution method. Substitute 2W-3 for L in the first equation.
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42=2L%2B2W
42=2%282W-3%29%2B2W
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Simplify by clearing the parentheses.
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42=4W-6%2B2W
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Combine like terms (4W+2w is 6W.)
42=6W-6
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We want to isolate the variable W on one side of the equation. Add 6 to both sides. Simplify.
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42%2B6=6W
48=6W
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Divide both sides of the equation by 6.
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48%2F6=6W%2F6
8=W
W=8
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In the context of this problem, the equation W=8 means that the width of the rectangle is 8m.
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Substitute 8 for W in either equation to find the length. I'll use the 2nd equation.
L=2W-3
L=2%288%29-3
L=16-3
L=13
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The length is 13m.
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STEP IV: Check your answers in the original problem.
The perimeter is 42. Two widths is 2*8=16. Two lengths is 2*13=26, and 16 plus 26 is 42. Check!
The length is 3 less than twice the width. Twice the width is 16 and 13 is 3 less than that. Check, check!!
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Hope this helps! Feel free to email if there is any part that does not make sense yet.
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Ms.Figgy
math.in.the.vortex@gmail.com

The perimeter of a rectangle in 42m. The length of the rectangle is 3m less than twice the width. Find the length and width of the rectangle.