total land area = 100 sq.m

Let the length be x m

then the width will be x+23 m

Since the plot is rectangular , therefore area is given by length *width

=> x(x+23) = 100

=>x^2+23x = 100

=>x^2+23x-100 = 0

On solving this quadratic equation you will get x = -26.7 or x=3.7

rejecting the negative value (as length or width cannot be negative),

Length is 3.7 m

width is 3.7 +23 = 26.7 m which is approximately 100 m.