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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

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Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

Fence It

Age 11 to 14 Challenge Level:
Choose a length for your rectangle.
What must the width be if the fence is $40$m long?
What's the area?

What happens to the area when you change your chosen length?