SOLUTION: 1. A rectangular piece of paper has area 100squrt2 cm^2. the piece is such that, when it is folded in half along the dashed line as shown, the new rectangle is similar (of the same

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 1. A rectangular piece of paper has area 100squrt2 cm^2. the piece is such that, when it is folded in half along the dashed line as shown, the new rectangle is similar (of the same      Log On


   

Question 767041: 1. A rectangular piece of paper has area 100squrt2 cm^2. the piece is such that, when it is folded in half along the dashed line as shown, the new rectangle is similar (of the same shape) to the original rectangle. What are the dimensions of the piece of paper?
2. simplify: %282%5E%28a%2B3%29+-+4%2A2%5Ea%29%2F+%282%5E%282a%2B1%29+-+4%5Ea%29
3. simplify, leaving answer with rational denominator
+sqrt%282%29%2F+%282sqrt%282%29+%2B+1%29+%2B+2%2F%28sqrt%283%29+%2B1%29+
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1. If the rectangular piece of paper looks like this: ,
the ratio of the sides is x%2Fy=y%2F2x, so
x%2Fy=y%2F2x --> 2x%5E2=y%5E2 --> y=xsqrt%282%29
and the area of the rectangle is
%282x%29y=100 --> %282x%29%28xsqrt%282%29%29=100 --> 2sqrt%282%29x%5E2=100 --> 8x%5E4=10000 --> x%5E4=1250 --> x%5E4=5%5E4%2A2 --> x=5root%284%2C2%29
So y=xsqrt%282%29 --> y=5root%284%2C2%29sqrt%282%29 --> y=5root%284%2C2%29root%284%2C4%29 --> y=5root%284%2C8%29

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