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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?

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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?

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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: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

The figure shows a rectangle PRSU with a line QT, which divides the rectangle into two squares.
How many right-angle triangles can be drawn using any three points P, Q, R, S, T, U as corners?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.