First, right down what you know in terms of variables.
#y = 2x + 3 #
#65 = y*x #
Next, choose one variable and substitute it in.
#"65 cm"^2 = (2x+3)*x#
#"65 cm"^2= 2x^2 +3x #
Move the #65# over and we can see the quadratic equation
#2x^2 +3x - 65 = 0#
Next factor.
#(2x+13)(x-5) = 0 #
#x = -"13 cm" or x = "5 cm"#
We know that the #x# value cannot be negative in this specific problem so we can eliminate the negative solution.
We plug our value for #x# into the first equation.
#y = 2("5 cm") + 3 #
#y = "13 cm"#
Now we check
#"65 cm"^2 = "13 cm" * "5 cm"#
which is true.
Thus the length is #"5 cm"# and the width is #"13 cm"#.
