We can solve this using the infamous Pythagorean Theorem which states that the sum of the squares of the legs equals the squares of the hypotenuse (the longest side). Using this we would square 3 and [tex]2 \sqrt{ x^{2} + 3x} [/tex] and take the square root of their sum.
[tex] 3^{2} = 9
[/tex]
[tex](2 \sqrt{ x^{2} + 3x} )^{2} = 4( x^{2} + 3x) = 4 x^{2} + 12x[/tex]
[tex] \sqrt{4 x^{2} + 12x + 9} = (2x + 3)[/tex]
Final Answer: c = 2x +3
