Question 114986: Carpentry:
The perimeter of the rectangular window is 14 ft. and its length is 2 ft less than twice the width. What are the dimensions of the window?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The perimeter of a plane figure is the sum of the lengths of its sides. Since you are told
that the figure is a rectangle you know that its sides are its length (call it L) and its
width (call it W) and by the definition of a rectangle there are two lengths and two widths.
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Therefore, you can write an equation for the perimeter (call it P) as:
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P = 2L + 2W
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And since you are told that the perimeter is 14 feet, you can substitute 14 for P to make
the equation become:
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14 = 2L + 2W
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Next you are told that its length is 2 feet less than twice its width. If the length equaled
twice its width you could say L = 2W, but the length is 2 feet less than 2W. So you can
write this equation as:
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L = 2W - 2
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Now you can return to the perimeter equation and substitute 2W - 2 for L because they are
equals. The perimeter equation is:
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14 = 2L + 2W
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Replace L with the quantity 2W - 2 and this equation becomes:
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14 = 2(2W - 2) + 2W
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Multiply out the first term on the right side of this equation and the equation becomes:
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14 = 4W - 4 + 2W
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On the right side combine the 4W and the +2W to get 6W and the equation then is:
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14 = 6W - 4
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Get rid of the -4 on the right side by adding +4 to both sides of the equation and the
equation then is:
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18 = 6W
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Solve for W by dividing both sides of the equation by 6 and you have:
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3 = W
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So W is 3 feet. Since there are two widths in the rectangle, the combined widths are 6
feet. Take that away from the perimeter and you have 14 - 6 = 8 feet. This remaining
8 feet is the dimension for the two lengths of the rectangle. So each length must be
half of 8 feet ... or you can say that the length of the window is 8 divided by 2 and this
is 4 feet.
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In summary, the width of the window is 3 feet and the length of the window is 4 feet.
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Check: The perimeter of the window is to be 14 feet. Add up the lengths and the widths:
4 + 4 + 3 + 3 and the sum is 14. So that requirement checks.
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Next the length is to be 2 feet less than twice the width. Twice the width is 2 times 3
which is 6 feet. Is the length (4 feet) 2 feet less than 6 feet. Yes, it is. So the answers
check out.
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Hope this helps you to see your way through the problem.
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