Find the side of the rhombus with diagonals equal to 24 dm and 70 dm.
| June 24, 2021 | education
1. The tops of the rhombus – A, B, C, D. AC = 70 decimeters. BD = 24 decimetres. E is the point of intersection of the diagonals.
2. ∠AED = 90 °, since the AC diagonal is perpendicular to the BD diagonal.
3. The diagonals of the rhombus at the intersection are divided into equal segments:
AE = 1/2 AC = 70: 2 = 35 decimeters.
DE = 1/2 BD = 24: 2 = 12 decimeters.
4. AD = √AE² + DE² (by the Pythagorean theorem).
AD = √35² + 12² = √1225 + 144 = √1369 = 37 decimeters.
Answer: the side of the rhombus is 37 decimeters.
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