Question 201850
If:
{{{A(x) = x^2+5x+6}}}
A) Find A(5)
{{{A(5) = 5^2+5*5+6}}}
{{{A(5) = 25+25+6}}}
{{{highlight(A(5) = 56)}}}
B) If the height (h) of the triangular sail is (x+3) meters, then what is the length of the base (b) of the sail?
Start with the formula for the area of a triangle:
{{{A = (1/2)b*h}}} Substitute {{{A = x^2+5x+6}}} and {{{h = x+3}}}
{{{x^2+5x+6 = (1/2)*b*(x+3)}}} Factor the trinomial on the left side.
{{{(x+2)(x+3) = (1/2)*b*(x+3)}}}  Divide both sides by (x+3).
{{{(x+2)*cross((x+3))/cross((x+3)) = (1/2)b}}} Cancel the common factors on the left side.
{{{x+2 = (1/2)b}}} Multiply both sides by 2.
{{{2x+4 = b}}} or {{{highlight(b = 2x+4)}}}