Question 534867
Start with:
{{{A = (1/2)b*h}}} for the area of a triangle. Substitute {{{A = 27}}}, {{{b = 4x+1}}}, and {{{h = 3x}}}
{{{27 = (1/2)(4x+1)(3x)}}} Simplify.
{{{27 = (1/2)(12x^2+3x)}}} Multiply both sides by 2.
{{{54 = 12x^2+3x}}} Subtract 54.
{{{12x^2+3x-54 = 0}}} Factor 3 to simplify.
{{{3(4x^2+x-18) = 0}}} Factor the trinomial.
{{{(4x+9)(x-2) = 0}}} Apply the zero product rule.
{{{4x+9 = 0}}} or {{{x-2 = 0}}} so...
{{{4x = -9}}} and {{{x = -9/4}}} or {{{x = 2}}} Discard the negative solution as this value of x ({{{x = -9/4}}}) would make the base and the height negative quantities.
{{{x = 2}}}