To find the base of the triangle, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
We know the area of the triangle is 33.75 square inches, and the height is 5 inches. Let's plug in the values and solve for the base.
\[ 33.75 = \frac{1}{2} \times \text{base} \times 5 \]
First, multiply both sides by 2 to eliminate the fraction:
\[ 2 \times 33.75 = \text{base} \times 5 \]
\[ 67.5 = \text{base} \times 5 \]
Next, divide both sides by 5 to solve for the base:
\[ \text{base} = \frac{67.5}{5} \]
\[ \text{base} = 13.5 \]
Thus, the base of Meredith's triangle is 13.5 inches.