SOLUTION: The perimeter of a rectangle is 100 m. The length is 18 m more than twice the width. Find the dimensions, length and width.

Question 461444: The perimeter of a rectangle is 100 m. The length is 18 m more than twice the width. Find the dimensions, length and width.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
First, think of the definition of perimeter as it applies to a rectangle. The perimeter is equal to the sum of the sides. In a rectangle there are two lengths and two widths. Let L represent the length and W represent the width. Therefore, you can write that the perimeter (P) is equal to:
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But you are told that the length is equal to 18 m more than twice the width. In equation form this is:
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So return to the perimeter equation and substitute 18 + 2W for L and the perimeter equation becomes:
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Perform distributive multiplication on the term inside the parentheses by multiplying 2 times each of the quantities inside the parentheses to get:
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Combine the two terms 4W and 2W by adding them to get 6W and the perimeter equation becomes:
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Now recognize that the problem tells you that the perimeter equals 100 m. So you can substitute 100 for P to get the equation:
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Get rid of the 36 on the right side of the equation by subtracting 36 from both sides and the equation reduces to:
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Now you can solve for the width W by dividing both sides of this equation by 6 and you have:
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Recognize that 0.66666666 ... is the decimal form of the fraction 2/3.
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and don't forget the units ... W, the width, is 10 and 2/3 meters.
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Now return to the equation that told you that the length, L, was 18 m longer than 2W. Since W is 10.6666666 ... meters, then twice W is 21.3333333 ... m and 18 m more than that is 18 + 21.33333333 ... = 39 and 1/3 m. So the length is 39 and 1/3 m. (Recognize again that 0.333333 ... is the decimal equivalent of the fraction 1/3.)
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Check to see that in a rectangle that is 39 and 1/3 meters long and 10 and 2/3 meter wide, the perimeter is 100 meters by adding up the four sides:
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If you do this addition, you will find that the sum is 100 meters so the solution you have is correct.
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Hope this helps you understand the problem a little better.
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