Question

Will give brainliest to correct answer.

Answer 1

Note that c is the hypotenuse of the blue triangle, and that the Pyth. Thm. states that (length of one leg)^2 + (length of the other leg)^2 = (hyp)^2.

Therefore, (hyp)^2 = c^2 = [2sqrt(x^2+3x)]^2 + 3^2, or
                                        = 4(x^2+3x) + 9, or
                                        = 4x^2 + 12x + 9  = (2x+3)^2
Taking the sqrt of both sides, c = plus or minus (2x+3).  Eliminate -(2x+3) because the middle term of the square of this would be negative, in conflict with the given +12x.

c=2x+3 is the correct answer.