Question 186558
Start with the formula for the area of a rectangle:
{{{A = L*W}}} Substitute {{{L = 4*W}}} "The length is four times the width."
{{{A = 4*W*W}}} Substitute A = 196 "The area is 196 sq. meters."
{{{4W^2 = 196}}} Subtract 196 from both sides.
{{{4w^2-196 = 0}}} Divide both sides by 4.
{{{W^2-49 = 0}}} This is the quadratic equation which can be solved by factoring.
{{{(W-7)(W+7) = 0}}} so that...
{{{W = 7}}} or {{{W = -7}}} Discard the negative solution as the width is a  positive quantity.
The width is 7 meters and the length is 4*7 = 28 meters.