Out of the window
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
Age
14 to 16
Challenge level
Problem
I have four rectangular pieces of thin hardboard whose dimensions (in cm) are 55 x 85, 65 x 75, 65 x 85, 90 x 105. Without bending the hardboard, how many of these can I get through an open rectangular window measuring 60 cm x 80 cm?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
By Pythagoras Theorem, the diagonal of the window is 100 cm, which exceeds the length or breadth of all the sheets. So the first three pieces can go through the window either way and the 90 x 105 cm piece can also go through the window, provided the 90 cm edge goes first.