Similar Triangles

The parallel sides of a trapezoid are 3 cm and 9 cm. The non parallel sides are 4 cm and 6 cm. A line parallel to the base divides the trapezoid into two trapezoids of equal perimeters. The ratio in which each of the non-parallel sides is divided is

The sides of a triangle are 30, 70 and 80 units. If an altitude is droped upon the side of length 80 units, the larger segment cut off on this side is

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio." This theorem is known as

"If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side." This theorem is known as converse of

ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is