SOLUTION: The perimeter of a rectangle is 42 cm. If the length is trebled and 7cm is added to 4 times the width, the perimeter of the new rectangle is 154 cm. Find the length of the original

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The perimeter of a rectangle is 42 cm. If the length is trebled and 7cm is added to 4 times the width, the perimeter of the new rectangle is 154 cm. Find the length of the original      Log On

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Question 1012979: The perimeter of a rectangle is 42 cm. If the length is trebled and 7cm is added to 4 times the width, the perimeter of the new rectangle is 154 cm. Find the length of the original rectangle.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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L=original length; W=original width;P=original perimeter
P2=perimeter of new rectangle
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P=2%28L%2BW%29
42cm=2%28L%2BW%29
21=L%2BW
21-W=L Use this to substitute below.
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P2=2%283L%2B4W%2B7%29
154cm=2%283L%2B4W%2B7%29
77=3L%2B4W%2B7
77=3L%2B4W%2B7 Substitute for L from above.
77=3%2821-W%29%2B4W%2B7
70=63-3W%2B4W
7=W
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ANSWER 1: The original width was 7 cm.
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L=21-W=21-7=14
ANSWER 2: The original length was 14 cm.
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CHECK:
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P=2%28L%2BW%29
P=2%2814cm%2B7cm%29
42cm=2%2821cm%29
42cm=42cm
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P2=2%283L%2B%284W%2B7%29%29
154cm=2%283%2814cm%29%2B4%287cm%29%2B7cm%29
154cm=2%2842cm%2B28cm%2B7cm%29
154cm=2%2877cm%29
154cm=154cm
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