SOLUTION: what is the ratio of the width to length of A folded sheet of paper if the rectangle formed when the sheet is folded in half is similar to the original rectangular sheet? express y

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Question 1043816: what is the ratio of the width to length of A folded sheet of paper if the rectangle formed when the sheet is folded in half is similar to the original rectangular sheet? express your answer as a common fraction in simplest radical form
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +L+ = the length of the paper
Let +W+ = the width of the paper
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I will fold the length side, so the new dimensions are:
+L%2F2+ by +W+
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I will say:
+%28+L%2F2+%29+%2F+W+=+W+%2F+L++
Multiply both sides by +L%2AW+
+L%5E2%2F2+=+W%5E2+
+L%5E2+=+2W%5E2+
Take the square root of both sides
+L+=+sqrt%282%29%2AW+
+W%2FL+=+1%2Fsqrt%282%29+
+W%2FL+=+sqrt%282%29%2F2+
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check answer:
Suppose +W+=+1+
+L+=+sqrt%282%29%2AW+
+L+=+sqrt%282%29+
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+%28+L%2F2+%29+%2F+W+=+W+%2F+L++
+%28+sqrt%282%29%2F2+%29+%2F+1+=+1+%2F+sqrt%282%29++
Multiply both sides by +sqrt%282%29+
+2%2F2+=+sqrt%282%29+%2F+sqrt%282%29+
+1+=+1+
OK