In isosceles right triangle, legs are equal. Let each leg is of x units . And the given hypotenuse is 5 square 6. We use pythagorean identity here, which is
[tex] a^2 + b^2 = c^2 [/tex]
Where a=b=x and c= 5 square root 6
[tex] x^2 +x^2 =(5 \sqrt6)^2 [/tex]
[tex] 2x^2 = 150 [/tex]
[tex] x^2 =75 [/tex]
[tex] x= 5 \sqrt 3 [/tex]
And that's the length of both the legs . ANd that's the required answer .
