A farmer wants to set aside a rectangular plot of land to contain 100 square meters. If the width is 23 more than the length, find the dimensions of the plot.
length=_____
width=_____
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.