Question 140925
A triangular sail with an area of: {{{A = x^2+5x+6}}} square meters and a height of: {{{h = x+3}}}meters, find the length of the sail's base.
Starting with the formula for the area of a triangle:
{{{A = (1/2)bh}}} Solve for b. Multiply both sides by 2.
{{{2A = bh}}} Divide both sides by h.
{{{b = 2A/h}}} Make the appropriate substitution:
{{{b = 2(x^2+5x+6)/(x+3)}}} Simplify.
{{{b = (2x^2+10x+12)/(x+3)}}} Perform the indicated division.
{{{b = 2x+4}}}
Check:
{{{A = (1/2)bh}}}
{{{x^2+5x+6 = (1/2)(2x+4)(x+3)}}} Use FOIL to multiply the binomials.
{{{x^2+5x+6 = (1/2)(2x^2+6x+4x+12)}}} Simplify the right side.
{{{x^2+5x+6 = (1/2)(2x^2+10x+12)}}} Perform the indicated multiplication.
{{{x^2+5x +6 = x^2+5x+6}}} Check!