Question

HELP PICTURE IS SHOWN

Answer 1

a^2+b^2=c^2

C is always the hypotenuse and the other two sides can be either a or b

19^2=361
12^2=144
361-144=217

Missing side EF equals$\sqrt{217}$

So A is the correct answer

Answer 2

The answer is:  [A]:  " √217 " .
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Explanation:
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Use the Pythagorean theorem:

For a right triangle:
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  a² + b² = c² ;
 
               in which:  
                                c = length of the hypotenuse; 
                                b = length of one of the side;
                                a = length of the other side;
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So,  a = ?  ;  (the value for which we wish to solve);
 
       b = 12 (given) ;
 
       c = 19 (given) ;
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  a² + 12² = 19²  ;  Solve for "a" 

  a² = 19² − 12² = 361 − 144 = 217
  
  a² = 217 ;

Take the positive square root of each side; (since a side of a triangle cannot be a "negative" value);  to isolate "a" on one side of the equation; and to solve for "a" ;
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    →   +√(a²)  =  +√(217) ;
 
    →    a = 14.7309198626562354

From the answer choices given, the correct answer choice is:
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Answer choice:  [A]:  " √217 " .
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