Answer
a) $x(x+6)=216$
b) Width: $12$ ft, length: $18$ ft
Work Step by Step
a) The area of the rectangle is the product between the length and the width:
$$x(x+6)=216$$
b) Determine $x$:
$$x^2+6x=216$$
$$x^2+6x+9=216+9$$
$$(x+3)^2=225$$
$$x+3=\pm\sqrt{225}=\pm15$$
$$x=\pm15-3$$
$$x_1=15-3=12~~~~$$
$$x_2=-15-3=-18$$
Take the positive value:
$$x=12$$
The dimensions are:
Length: $x+6=12+6=18$
Width: $x=12$
