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What fractions can you find between the square roots of 65 and 67?

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Equal Equilateral Triangles

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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The Square Hole

Age 14 to 16 Challenge Level:

Can you think of a reason why the yellow and purple triangles are equal in area ?

If the side length of the yellow triangle is taken as the unit for length, what length is the third side of the purple isosceles triangles ?