Find the side of the rhombus if its diagonals are 16 dm and 30 dm.

univerkov | September 16, 2021 | education

1. The tops of the rhombus – A, B, C, D. AC = 30 decimeters. VD = 16 decimeters. О is the point of intersection of the diagonals.

2. ∠APE = 90 °, since the AC diagonal is perpendicular to the VD diagonal.

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

AO = 1/2 AC = 30: 2 = 15 decimeters.

DO = 1/2 BD = 16: 2 = 8 decimeters.

4. AD = √AO² + DO² (by the Pythagorean theorem).

AD = √15² + 8² = √225 + 64 = √289 = 17 decimeters.

Answer: the side of the rhombus is 17 decimeters.

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