### Right Time

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

### Isosceles

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.

The length of each side of a quadrilateral $ABCD$ is a whole number of centimetres. Given that $AB=4 \; \text{cm}$, $BC = 5 \; \text{cm}$ and $CD = 6 \; \text{cm}$, what is the maximum possible length of the fourth side $DA$?