Question 701526
The sides of a 45-45-90 triangle have ratios {{{ 1 }}} : {{{ 1 }}} : {{{ sqrt(2) }}}
You are given the side opposite the 90 angle is {{{ 6 }}}
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If you multiply the ratios by a constant, the ratios do not change, so
{{{ k*1 }}} : {{{ k*1 }}} : {{{ k*sqrt(2) }}}  still describe a 45-45-90 triangle
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What if I say {{{ k = 6/sqrt(2) }}} ? I then have
{{{ 6/sqrt(2) }}} : {{{ 6/sqrt(2) }}} : {{{ ( 6/sqrt(2) )*sqrt(2) }}} and simplifying:
{{{ 6/sqrt(2) }}} : {{{ 6/sqrt(2) }}} : {{{ 6 }}}
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so, the missing sides are {{{ 6/sqrt(2) }}}, and simplifying:
{{{ ( 6/sqrt(2))*( sqrt(2) / sqrt(2) ) }}} 
{{{ ( 6*sqrt(2) ) / 2 }}} 
{{{ 3*sqrt(2) }}} answer
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check answer:
{{{ 6^2 = ( 3*sqrt(2) )^2 + ( 3*sqrt(2) )^2 }}}
{{{ 36 = 9*2 + 9*2 }}}
{{{ 36 = 18 + 18 }}}
{{{ 36 = 36 }}}
OK