Determine the missing side length:

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The answer is:  "3" .

Use the Pythagorean theorem (for right triangles):

a² + b² = c² ;

in which "a = "side length 1" (unknown; for which we which to solve);

               "b" = "side length 2" = "√3" (given in the figure) ;

               "c" = "length of hypotenuse" = "2√3" (given in the figure);

a² + b² = c² ; 

a² = c² − b² ;

Plug in the known values for "c" and "b" ;

a² = (2√3)²  −  (√3)² ;

Simplify:

(2√3)² = 2² * (√3)² = 2 * 2 * (√3√3)  = 4 * 3 =  12 .

 (√3)²  = (√3√3) = 3 .

a²  = 12 − 3 = 9 .

a² = 9

Take the "positive square root" of EACH SIDE of the equation; to isolate "a" on one side of the equation;  & to solve for "a" ; 

+√(a²)  = +√9 ;

     a = 3 . 

The answer is:  "3" .

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