Problem B. 4691. (February 2015)

B. 4691. \(\displaystyle a\), \(\displaystyle b\), \(\displaystyle c\) and \(\displaystyle d\) are four parallel lines in the plane, in this order. The distance of \(\displaystyle a\) and \(\displaystyle b\) is 1, the distance of \(\displaystyle b\) and \(\displaystyle c\) is 3, and the distance of \(\displaystyle c\) and \(\displaystyle d\) is also 1. Consider the rectangles that have exactly one vertex on each line. How can we obtain the rectangle of minimal area, and what is this area?

(3 pont)

Deadline expired on March 10, 2015.

Statistics:

129 students sent a solution.
3 points:	86 students.
2 points:	18 students.
1 point:	15 students.
0 point:	9 students.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, February 2015