Rectangle Perimeter Problem: Using Triangle Area of 9 to Find Solution

Look at the following rectangle:

Given that the area of the triangle ABD is 9, what is the perimeter of the rectangle ABCD?

Area of triangle ADB:

$\frac{AD\times AB}{2}$

Let's list the known data:

$9=\frac{x+2\times6}{2}$

$9=(x+2)\times3$

$9=3x+6$

$9-6=3x$

$3=3x$

$1=x$

Side AD equals:

$1+2=3$

Since in a rectangle, each pair of opposite sides are equal, we can state that:

$AD=BC=3$

$AB=CD=6$

Now we can calculate the perimeter of the rectangle:

$3+6+3+6=6+12=18$