Question 35558
area of triangle  = (1/2)*b*h where b is the length of base and h is the height
area is given to be x^2 +5x + 6
height  = x+3

1/2*b*(x+3) = x^2 + 5x + 6

The right side x^2 +5x + 6  can be factorised as (x+3)(x+2)

(1/2)*b*(x+3) = (x+3)(x+2)

cancelling (x+3) on both sides leaves
(1/2)*b = x+2
b = 2*(x+2) = 2x+4
The length of the base is 2x+4