Question 478929
Start with the formula for the area of a rectangle of length L and width W:
{{{A = L*W}}} Substitute {{{A = 55}}}, {{{L = x+8}}}, and {{{W = x+2}}} to get:
{{{55 = (x+8)(x+2)}}} Simplify.
{{{55 = x^2+10x+16}}} Subtract 55 from both sides.
{{{x^2+10x-39 = 0}}} Factor.
{{{x-3)(x+13) = 0}}} Apply the "zero product" rule.
{{{x-3 = 0}}} or {{{x+13 = 0}}} so...
{{{x = 3}}} or {{{x = -13}}} Discard the negative solution as length and width are positive values.
{{{x = 3}}}
{{{L = x+8}}} Substitute {{{x = 3}}}
{{{highlight(L = 11)}}}
{{{W = x+2}}} Substitute {{{x = 3}}} 
{{{highlight(W = 5)}}}