Question 293217
The area of a rectangle is given by:
{{{A = L*W}}} Substitute {{{L = (x+6)}}}, {{{W = (x+3)}}}, and {{{A = 40}}}
{{{40 = (x+6)(x+3)}}} Perform the multiplication.
{{{40 = x^2+9x+18}}} Subtract 40 from both sides.
{{{x^2+9x-22 = 0}}} Solve this quadratic equation by factoring.
{{{(x+11)(x-2) = 0}}} Apply the "zero product" rule.
{{{x+11 = 0}}} or {{{x-2 = 0}}} so that...
{{{highlight(x = -11)}}} or {{{highlight_green(x = 2)}}} Discard the negative solution as the dimensions cannot be negative.
{{{L = x+6}}} Substitute x = 2.
{{{L = 2+6}}}
{{{highlight_green(L = 8)}}} and...
{{{W = x+3}}} Substitute x = 2.
{{{W = 2+3}}}
{{{highlight_green(W = 5)}}}