Question 1043816
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/2 }}} by {{{ W }}}
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I will say:
{{{ ( L/2 ) / W = W / L  }}}
Multiply both sides by {{{ L*W }}}
{{{ L^2/2 = W^2 }}}
{{{ L^2 = 2W^2 }}}
Take the square root of both sides
{{{ L = sqrt(2)*W }}}
{{{ W/L = 1/sqrt(2) }}}
{{{ W/L = sqrt(2)/2 }}}
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check answer:
Suppose {{{ W = 1 }}}
{{{ L = sqrt(2)*W }}}
{{{ L = sqrt(2) }}}
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{{{ ( L/2 ) / W = W / L  }}}
{{{ ( sqrt(2)/2 ) / 1 = 1 / sqrt(2)  }}}
Multiply both sides by {{{ sqrt(2) }}}
{{{ 2/2 = sqrt(2) / sqrt(2) }}}
{{{ 1 = 1 }}}
OK