#### You may also like ### Ladder and Cube

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? Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load. ### Three Cubes

Can you work out the dimensions of the three cubes?

# Right-angled Midpoints

##### Age 14 to 16 Short Challenge Level: $FGH$ is a right angled triangle with shortest sides $FH = 6\text{cm}$ and $FG = 8\text{cm}$.

$I$, $J$, and $K$ are the mid points of the sides $GH$, $FH$ and $FG$ respectively.

What is the perimeter of the triangle $IJK$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.