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.
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