A Rectangle with vertices A B C AND D. The triangle is divided with vertices P AND Q. How many right triangles can you make with using only three of the vertices {A B C D P OR Q}. AND also the answer for this question is not 12 or 6

To find the number of right triangles that can be formed using three of the given vertices of the rectangle and the divided triangle, we need to consider all possible combinations of three points and check if they form a right triangle.

Step 1: Identify the possible combinations of three vertices:
- We have four vertices of the rectangle (A, B, C, D) and two vertices of the divided triangle (P, Q).
- In total, there are 6 possible combinations of three vertices: (ABC), (ABD), (ACP), (ADP), (BCP), (BDP).

Step 2: Check if the formed triangle is a right triangle:
- To determine if a triangle is a right triangle, we can check if the square of the longest side is equal to the sum of the squares of the other two sides (using the Pythagorean theorem).
- Calculate the squares of the lengths of the sides for each of the six triangles: AB, AC, AD, BC, BD, CP, DP.
- Check if the square of the longest side is equal to the sum of the squares of the other two sides for each triangle.

Step 3: Count the number of right triangles:
- Count how many of the triangles from step 2 satisfy the Pythagorean theorem.
- The total count will give us the answer.

Considering that the answer is not 12 or 6, you would need to perform the above steps and determine the correct count of right triangles that can be formed using the given vertices.