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 two poles 2 m and 8 m high are 100 m apart, then the height of the point of intersection of the line joining the top of each pole to the foot of the opposite pole is

Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal of the field and saved a distance equal to 1/2 of the longer side. The ratio of the shorter side of the rectangle to the longer side is

Side AC of right triangle ABC is divided into 8 equal parts. Seven line segments parallel to BC are drawn from the points of divisions. If BC = 10 cm, then the sum of lengths of the seven line segments is