Rectangle is divided into 14 identical smaller rectangles of width $x$. What is its perimeter in terms of $x$?

Question

Rectangle region ABCD show in below partitioned into 14 identical small rectangles, each of which has width x.

What is perimeter of ABCD in terms of x?

I have used rectangle perimeter formula but answer getting wrong . what is method to find answer in shortest way ?

Answer 1

If each small rectangle has width $x$, then we can see that the length of the small rectangles is 7 widths of the small rectangle, thus $7x$. Therefore, sides $AP$, $DQ$ and $BC$ have length $7x$. Finally, $AD$, $QC$, and $PB$ have length $7x$. Thus, we have six sides with length $7x$, so the perimeter has length $6\cdot 7x = 42x$.