Keep your distance

Geometry Level 5

Let ΔABC\Delta ABC have integer side lengths and be right-angled at BB. Now suppose ΔDEF\Delta DEF is located within ΔABC\Delta ABC with the same orientation, such that its sides are parallel to the corresponding sides of ΔABC\Delta ABC and the distance between the corresponding parallel sides is 33.

If the area of ΔABC\Delta ABC is 44 times that of ΔDEF\Delta DEF then there are nn possible triangles ΔABC\Delta ABC independent of orientation. If SS is the sum of the lengths of the hypotenuses of these nn triangles, then find n+S.n + S.

×

Problem Loading...

Note Loading...

Set Loading...