It might be helpful to start by plotting the points and the line you are given.
Can you find the equation of a line from two points? Do you know how to find the gradient of a line perpendicular to another line?
The point C must lie on the line which is perpendicualr to AB and passes through point B (1,6).
Using the points A and B you can find the equation of AB and then BC, see above.
AC is a diagonal of the rectangle and you can find the point C by finding the intersection of the lines AC and BC.
If you plot the co-ordinates of A, B and C you might be able to see how to find the perimeter.
Can you proceed from here. Please ask if you need more help.