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