Question 85459
Since we have a triangle with legs of 8 , x(our unknown side) and a hypotenuse of 12, we can use Pythagoreans theorem to find the unknown side.

Pythagoreans theorem
{{{a^2+b^2=c^2}}}


{{{8^2+b^2=12^2}}}  Plug in a=8 and c=12 and lets solve for b

{{{6 4 +  b  ^ 2 = 1 4 4}}} Square each individual term




{{{ b  ^ 2 = 1 4 4 - 6 4}}} Subtract 64 from both sides



{{{ b  ^ 2 = 8 0}}} Combine like terms



{{{s q r t (  b  ^ 2 ) = s q r t ( 8 0 )}}} Take the square root of both sides



{{{b = s q r t ( 8 0 )}}} 


{{{b=4*sqrt(5)}}} Simplify


So our answer is

{{{b=4*sqrt(5)}}}