Question 316201
Length is six times the width: {{{ L = 6 * W }}} (eq 1) 

Perimeter is the sum of the lengths of all four sides. Remember that for a rectangle, the opposite sides have the same length. There are two sides which have length L and two sides of W. The perimeter is {{{ P = 2 L + 2 W} = 84}} (eq 2). 

Substitute (eq 1) into (eq 2), which gives {{{2 (6W) + 2 W = 12 W + 2 W = 14 W = 84 }}}. 

Since {{{14W=84}}}, divide both sides by 14 to get {{{W = 6}}}. 

Now we should check: Since W = 6, and L=6*W, we know that L=36. Then the perimeter is P=2L+2W=2*36+2*6=72+12=84, so it checks out.