1. **State the problem:** We have a right triangle with base $a$ and hypotenuse 18. A segment from the right angle perpendicular to the hypotenuse divides it into two parts, the larger part being 16. 2. **Identify the relevant property:** In a right triangle, the altitude to the hypotenuse creates two smaller right triangles similar to the original triangle and to each other. 3. **Use the similarity property:** The segments into which the hypotenuse is divided relate to the legs of the triangle. The leg $a$ corresponds to the segment adjacent to it on the hypotenuse. 4. **Set up the proportion:** The leg squared equals the product of the hypotenuse and the adjacent segment. So, $$a^2 = 18 \times 16$$ 5. **Check the options:** Option B is $a^2 = 16a$, which is incorrect because the right side should be $18 \times 16$, not $16a$. Option A is $34a = a16$, which is not a valid proportion. Option C is $a18 = 2a$, which is incorrect. Option D is $18a = a16$, which is also incorrect. 6. **Conclusion:** None of the options exactly match the correct proportion $a^2 = 18 \times 16$. However, the closest correct form is $a^2 = 18 \times 16$, which is not listed. The problem likely intends option B but with a typo. **Final answer:** The correct proportion to find $a$ is $$a^2 = 18 \times 16$$.