Triangle Inscribed in A Rectangle
Leaving 3 Right Triangles of Equal Area
Given a rectangle of length a and width b.
Inscribe a triangle with one vertex coinciding with a vertex of the rectangle and each of the other two verticies on an opposite sides so that three right triangles and the inscribed triangle cover the rectangle.
Problem 1. Let ABCD be the rectangle and inscribe triangle APQ such that P is on BC and Q is on CD. We want to locate P and Q such the right triangles ABP, ACQ and QDA all have the same area. How do we locate P and Q.
Note: It is NOT given that Triangle APQ is a right triangle. Could it be a right triangle?
If so, must it be a right triangle?
Problem 2. What if we had the additional condition that triangle APQ is isoscles with AP = AQ?
Hint:
Label the figure as at the right and use the given condition that the three right triangles have equal area.