Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
Can you make a tetrahedron whose faces all have the same perimeter?
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?
The diagram shows a triangle and three circles whose centres are at the vertices of the triangle. The area of the triangle is $80 cm^2$ and each of the circles has radius $2cm$. What is the area, in $cm^2$, of the shaded area?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic