The rectangle in the figure has dimensions $16$ x $20$ and is divided into $10$ smaller equal rectangles. What is the perimeter of each of the $10$ smaller rectangles?
1. **Identify the dimensions of the large rectangle:**
   The large rectangle has dimensions \(16 \times 20\).

2. **Determine the area of the large rectangle:**
   \[
   \text{Area of the large rectangle} = 16 \times 20 = 320
   \]

3. **Determine the area of each smaller rectangle:**
   Since the large rectangle is divided into 10 smaller equal rectangles, the area of each smaller rectangle is:
   \[
   \text{Area of each smaller rectangle} = \frac{320}{10} = 32
   \]

4. **Assume the dimensions of the smaller rectangles:**
   Let \(x\) be the length of the longer side and \(y\) be the length of the shorter side of each smaller rectangle. Then:
   \[
   x \times y = 32
   \]

5. **Determine the possible configurations:**
   Since the large rectangle is divided into 10 smaller rectangles, we need to consider how these smaller rectangles are arranged. One possible configuration is to have 2 rows and 5 columns of smaller rectangles. This means:
   \[
   2y = 16 \quad \text{(height of the large rectangle)}
   \]
   \[
   5x = 20 \quad \text{(width of the large rectangle)}
   \]

6. **Solve for \(x\) and \(y\):**
   \[
   2y = 16 \implies y = \frac{16}{2} = 8
   \]
   \[
   5x = 20 \implies x = \frac{20}{5} = 4
   \]

7. **Calculate the perimeter of each smaller rectangle:**
   The perimeter \(P\) of a rectangle is given by:
   \[
   P = 2(x + y)
   \]
   Substituting the values of \(x\) and \(y\):
   \[
   P = 2(4 + 8) = 2 \times 12 = 24
   \]

The final answer is \(\boxed{24}\).