### 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.

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?

# Anulus Area

##### Stage: 3 and 4 Short Challenge Level:

Ans: 28%

The area of the larger circle is 25$\pi$ cm $^2$.
The area of the smallest circle is 9$\pi$ cm $^2$.
The area of the middle circle is 16$\pi$ cm $^2$.
Therefore the area of the ring is (16$\pi$ - 9 $\pi$) cm $^2$ i.e. 7\ $\pi$ cm $^2$.

Therefore the percentage shaded is 28%.

This problem is taken from the UKMT Mathematical Challenges.
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