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Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

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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?

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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Isosceles

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 isosceles triangles which are not congruent but have equal areas.

How many isosceles triangles have an area of 12 square units?


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