In a rhombus, a height drawn from the top of an obtuse angle divides the side in half.

In a rhombus, a height drawn from the top of an obtuse angle divides the side in half. find the perimeter of the rhombus if the length of the shorter side is 20 dm.

1. An error was made in the problem statement. 20 inches is the length of the smaller diagonal BD (not the side).

2. A, B, C, D – the tops of the rhombus. BH is the height drawn from the top of the blunt ABC. BD = 20 dm.

3. Since the height BH divides the side AD into two equal segments, it is also the median, and the triangle ABD is isosceles, that is, AB = BD = 20 dm.

4. We calculate the total length of all sides of the rhombus (perimeter P), taking into account that all sides of the rhombus are equal:

P = 4AB = 4 x 20 = 80 dm.

Answer: the perimeter of the rhombus is 80 dm.