Triangles Inside a Rectangle

Examine the area and perimeter of a triangle compared to a rectangle. Rationalize this!: Find the a right triangle with rational side lengths, and a hypotenuse numerically equal to the area of the triangle. Equal Areas: Determine why a certain rectangle has the same area as a triangle. Optimal Triangles: Determine the largest area of…



A triangle has two shared vertices and one shared side with a rectangle. The third vertex is anywhere on the side opposite of the shared side (see figures above).
How does the area of the triangle compare with the area of the rectangle? Why do you think this relationship holds?

Extension:
Where would you move the third vertex of the triangle to have a minimum perimeter? Explain why this position results in a minimum perimeter.