Question 457307
First using Pythagorean Theorem we find the diagonal of one side:

{{{10^2+10^2=x^2}}}=>{{{x=10sqrt(2)}}}cm. Using again the Pythagorean Theorem

we find the diagonal of the cube:{{{d^2=(10sqrt(2))^2+10^2}}}=>{{{d^2=sqrt(300)}}}

=>{{{d=10sqrt(3)}}}cm.

Answer:The diagonal of the cube is {{{10sqrt(3)}}}cm.