All black triangles in the picture are equilateral.
What is the ratio of sides of the outer and inner squares?
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We have seen how we can draw a series of right triangles as in the picture. What are the lengths of the sides of the tenth triangle? .

What is the circum radius of an equilateral triangle of sides 8 centimetres?

A square is drawn on the altitude of an equilateral triangle of side 4 cm. a) What is the altitude of the triangle? b) What is the area and perimeter of the square?

A square is drawn on the altitude of an equilateral triangle of side 2 metres. What is the area of the square? .

A 50 centimetre long rod is to be cut into two pieces, one of which is to be bent to form a square and other is to be bent to form an equilateral triangle. The length of a side of the equilateral is twice the length of the side of a square. Find the length of the side of a square and equilateral triangle.

In the picture below, the top vertex of a triangle is joined to the midpont of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices: Prove that the areas of all three triangles in the picture on the are equal to a third of the area of the whole triangle.

In the picture below, the top vertex of a triangle is joined to the midpoint of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices. Prove that the areas of all three triangles in the picture on the right are equal to a third of the area of the whole triangle