Tennis

A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

Tied Up

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal can reach all points in the field. Which one is it and why?

How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Right-angled Request

Stage: 3 Short Challenge Level:

Four right-angled triangles can be drawn in each of the squares, plus four formed from two adjacent sides of the rectangle - that makes 12.

Then there are two right-angled triangles formed by joining the points UQS and PTR.

This makes a total of 14 triangles.

This problem is taken from the UKMT Mathematical Challenges.
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