Question 119405
Start with the formula for the perimeter of a rectangle:
{{{P = 2(L+W)}}} Substitute: {{{L = 2W+6}}}
{{{P = 2((2W+6)+W)}}} Simplify.
{{{P = 4W+12+2W}}}
{{{P = 6W+12}}} Substitute {{{P = 78}}}
{{{78 = 6W+12}}} Subtract 12 from both sides.
{{{66 = 6W}}} Divide both sides by 6.
{{{11 = W}}} The width is 11 inches.
{{{L = 2W+6}}} Substitute {{{W = 11}}}
{{{L = 2(11)+6}}}
{{{L = 22+6}}}
{{{L = 28}}} The length is 28 inches.
Check:
{{{P = 2(L+W)}}} Substitute {{{L = 28}}} and {{{W = 11}}}
{{{P = 2(28+11)}}}
{{{P = 2(39)}}}
{{{P = 78}}} OK!