A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't fight
each other but can reach every corner of the field?
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
Age 11 to 14 Challenge Level:
The smallest right-angled triangle where the lengths of all the
sides are integers, has sides of length $3$, $4$ and $5$ units.
This triangle has an area of $6$ square units and a perimeter of
How many right-angled triangles are there with sides that are
all integers less than $100$ units?
In how many of these triangles is the area one half of the
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.