Question 633612
Let L = length and W = width.
{{{L = 2W+1}}} "The length of a rectangle is 1m longer than twice the width."
The area of a rectangle is given by:
{{{A = L*W}}} Substitute {{{L = 2W+1}}} and {{{A = 105}}}.
{{{105 = (2W+1)*W}}} Simplify.
{{{105 = 2W^2+W}}} Subtract 105 from both sides.
{{{2W^2+W-105 = 0}}} Solve this quadratic equation by factoring.
{{{(2W+15)(W-7) = 0}}} Apply the "zero product" rule.
{{{2W+15 = 0}}} or {{{W-7 = 0}}}
{{{2W = -15}}} or {{{W = 7}}} Discard the negative solution as the width, W is a positive quantity.
{{{W = 7}}} and {{{L = 2(7)+1}}}={{{15}}}