Question 1054511
By the pythagorean theorem:
{{{ x^2 + x^2 = 10^2 }}}
{{{ 2x^2 = 10^2 }}}
{{{ x^2 = 10^2/2 }}}
Take the square root of both sides
{{{ x = sqrt( 10^2/2 ) }}}
{{{ x = 10/sqrt(2) }}}
Usually, you don't want square roots
or other roots on the bottom, so do this:
{{{ x = ( sqrt(2) / sqrt(2) )*( 10/sqrt(2) ) }}}
{{{ x = 10*sqrt(2) / 2 }}}
{{{ x = 14.14/2 }}}
{{{ x = 7.07 }}}
-----------------
check:
{{{ 2*7.07^2 = 10^2 }}}
{{{ 2*49.98 = 100 }}}
{{{ 99.97 = 100 }}}
( error due to rounding off )
OK