Question 1080017
the leg of an isosceles right triangle are same length: leg {{{a}}} is equal to 
leg {{{b}}},  {{{a=b}}}

if the hypotenuse is {{{h = 5sqrt( 6)}}}, using Pythagorean theorem we have


{{{h^2=a^2+b^2}}}........since  {{{a=b}}} and {{{h = 5sqrt( 6)}}}, we have


{{{5sqrt( 6)=a^2+a^2}}}


{{{5sqrt( 6)=2a^2}}}


{{{5sqrt( 6)/2=a^2}}}


{{{sqrt(5sqrt( 6)/2)=a}}}


{{{a=(1/2)*root(4,6)*sqrt(10)}}}


approximately:
{{{a=2.48}}} and {{{b=2.48}}}