Question

HELP PICTURE IS SHOWN

Answer 1

The answer is: [A]: " √217 " .
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Step-by-step 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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Answer 2

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
`√(217)`

So A is the correct answer