Two legs are 3√2. the triangle is 45-45-90. what is the hypotenuse? a. 6b. 18c. 12d. 5

The answer is:   [A]:  "6" .

Explanation:


Using the Pythagorean theorem to solve for the hypotenuse of a right triangle:

                a² + b² = c² ;

in which "c" is the length of the "hypotenuse" (for which we are to solve);
   & "a" and "b" are the lengths of the other 2 (two) sides.

In this case, "a" and "b" are "equal lengths" ; 

that is:  a = b = 3√2 ;

So "(3√2)² + (3√2)² = c² " ; Solve for "c" ; 

↔  c² = (3√2)² + (3√2)² ; 

→  c² = 2*(3√2)² = 2 * (3²) * (√2)² ;

                            =  2 * 9 * 2 ; 

                            = 18 * 2 = 36 ;

→ c² = 36 ; 

Take the positive square root of each side of the equation ; to isolate "c" on one side of the equation ; & to solve for "c"  (the length of the hypotenuse);

→  +√(c²) = +√36 ; 
  
      →  c = 6  ;  which is:  "Answer choice:  [A]:  "6" .