Question 154433
Remember the area of any triangle is: Area = (1/2)(Base * Height)



{{{A = (1/2)(b*h)}}} Start with the given formula.



{{{x^2 + 5x + 6 = (1/2)(b)(x + 3)}}} Plug in the given area {{{A=x^2 + 5x + 6 }}} and the height {{{h=x+3}}}



{{{(x^2 + 5x + 6)/(x + 3)= (1/2)*(b)}}} Divide both sides by {{{x+3}}}



{{{((x+3)(x+2))/(x + 3)= (1/2)*(b)}}} Factor {{{x^2 + 5x + 6}}} to get {{{(x+3)(x+2)}}}



{{{(cross((x+3))(x+2))/cross((x+3))= (1/2)*(b)}}} Cancel the common terms.



{{{x+2= (1/2)*(b)}}} Simplify



{{{2(x+2)= b}}} Multiply both sides by 2.



{{{2x+4= b}}} Distribute



So the base is {{{b=2x+4}}}