To find the perimeter of a rectangle, you can use the formula:
\[
P = 2 \times (length + width)
\]
In this case, the left side of the rectangle is given as \(5x - 4\) (height), and the bottom as \(3x + 10\) (width).
First, we need to add the lengths of the sides together:
\[
\text{Length} + \text{Width} = (5x - 4) + (3x + 10)
\]
Combine like terms:
\[
= 5x + 3x - 4 + 10
\]
\[
= 8x + 6
\]
Now, substitute back into the perimeter formula:
\[
P = 2 \times (8x + 6)
\]
Distribute the 2:
\[
P = 16x + 12
\]
So, the expression that represents the perimeter of the rectangle is:
**16x + 12**
The correct option is:
**16x + 12**