Find the perimeter of a rhombus if its diagonals are 60 and 80 cm.

1. A, B, C, D – the vertices of the rhombus. Diagonals AC and BD are 80 cm and 60 cm, respectively. O is the point of their intersection. P is the perimeter.

2. Triangle AOD is rectangular since the diagonals are perpendicular. Angle AOD = 90 °.

3. The diagonals at the intersection point are divided into equal segments:

AO = 1/2 AC = 80: 2 = 40 cm.

DO = 1/2 BD = 60: 2 = 30 cm.

3. AD² = AO² + DО² (by the Pythagorean theorem).

AD = √40² + 30² = √1600 + 900 = √2500 = 50 cm.

4. Each side of the rhombus is 50 cm.

5.R = 4 x 50 = 200 cm.

Answer: P = 200 cm.