Question 202532
If {{{A(x) = x^2+5x+6}}}:
1) Find {{{A(5)}}} Substitute x = 5 into the given equation for the area.
{{{A(5) = (5)^2+5(5)+6}}} Evaluate.
{{{A(5) = 25+25+6}}}
{{{A(5) = 56}}}sq.meters.
2) Use the formula for the area of a triangle:
{{{A = (1/2)*b*h}}} Substitute: {{{A = x^2+5x+6}}}, {{{h = x+3}}}
{{{x^2+5x+6 = (1/2)*b*(x+3)}}} Multiply both sides by 2.
{{{2x^2+10x+12 = b*(x+3)}}} Factor the left side.
{{{(2x+4)(x+3) = b*(x+3)}}} Divide both sides by (x+3)
{{{((2x+4)*cross((x+3)))/cross((x+3)) = b}}} Cancel the common factors.
{{{highlight(b = 2x+4)}}}