Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Golden Thoughts

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 golden ratio.

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?

3-sided

Stage: 3 and 4 Short Challenge Level:

Jack's teacher asked him to draw a triangle of area $7\textrm{ cm}^2$. Two sides are to be of length $6\textrm{ cm}$ and $8\textrm{ cm}$. How many possibilities are there for the length of the third side of the triangle?

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.

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