help solve missing side of triangle

Question

please help me solve to find the missing side of a triangle.  One side is 1/2x + 11 and the other side is 2x + 1.  The missing side is labled as ,x, .

 

Would I start as a^2 + b^2 = c^2?

Answer 1

Is this a right triangle? If so, which side is the hypotenuse?

 

If it is a right triangle and you know which side is c, then you can use the Pythagorean Theorem.

Answer 2

If you do not know it's a right triangle...

 

The sum of any two sides must be larger than the third.

 

 

x + (.5x + 11) > 2x + 1

 

x< 20

 

x + (2x+1) > .5x + 11

x > 4

 

 

4 < x < 20

Answer 3

X >0

 

  ( 2X +1 )^2 = (1/2 X+ 11) ^2 + X^2

 

 

  4X^2 + 4X +1 = 1/4 X^2 +11X +121 +X^2

 

  11/4 X^2 -7X -120 = 0

 

    11 X^2 -28X -480 =0

    

    11 X^2 - 88X + 60X -480 =0

 

     11X( X - 8 ) + 60 ( X -8 ) =0

 

      ( X - 8 ) ( 11X +60 ) =0

 

          ( X -8 ) =0    X =8

 

        Negative answer is not acceptable .