Question 515129
The triangle ABC is an isosceles right triangle this means that the legs are equal
Using the Pythagorean theorem we write:

{{{x^2+x^2=5^2}}} where x is the length of each leg. Solving the equation we get:

{{{2x^2=25}}}

{{{x^2=25/2}}}

{{{x=sqrt(25/2)}}}

{{{x=5/sqrt(2)}}} Rationalizing the denominator {{{x=5*sqrt(2)/2}}}

Answer: The length of segment BC is {{{5*sqrt(2)/2}}}