A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the track.
Patrick from Woodbridge School offered the
following insight to this problem, as did Chip from King's Ely
An anonymous solver also wrote:
The long thin parallelogram occurs because the
slopes of the trapezia are not the same as explained by Patrick and
Chip: the slopes of the triangles. For each trapezium the slope is
in the ratio of 2 up to 5 across and for each triangle the slope is
in the ratio of 3 up to 8 across.
Finally, Susie from DEECD Victoria
offered an example of other numbers that work (Do they have the
same properties as the numbers used for the lengths in the
problem?). She said: