Question 22819
I can see why you're having trouble solving this problem.
Your opening statement..."The length of a rectangle is 6 times more than its width..." implies that the length, L = 6W but what I believe you should have written is..."The length is 6 more than its width..." which would translate into L = W + 6,  So let's work it on that assumption.

A = L*W but L = W+6, so:
A = (W+6)*W = 72 cm^2 Simplify and solve for W
{{{W^2 + 6W = 72}}} Subtract 72 from both sides of the equation.
{{{W^2 + 6W - 72 = 0}}} Solve this quadratic equation by factoring.
{{{(W + 12)(W - 6) = 0}}} Apply the zero product principle.
{{{(W + 12) = 0}}} and/or {{{(W - 6) = 0}}}
If {{{W + 12 = 0}}} then, {{{W = -12}}} Discard this solution, width must be positive.
If {{{W - 6 = 0}}} then, {{{W = 6}}} The width is 6 cm.