Question 120406
Remember the area of any triangle is: {{{A=(b*h)/2}}}



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



{{{x^2 + 5x + 6=(b*(x+3))/2}}} Plug in {{{A=x^2 + 5x + 6}}} and {{{h=x+3}}}




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




{{{2(x+3)(x+2)=b(x+3)}}} Multiply both sides by 2



{{{2(x+3)(x+2)/(x+3)=b}}} Divide both sides by {{{x+3}}} to isolate b




{{{2cross((x+3))(x+2)/cross((x+3))=b}}} Cancel like terms




{{{2(x+2)=b}}} Simplify



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




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