The perimeter of the rhombus is 52 cm, one of its diagonals is 10 cm. Find the second diagonal of the rhombus.
| March 19, 2021 | education
1. A, B, C, D – the vertices of the rhombus. AC = 10 cm. Diagonals intersect at point O. P – perimeter.
2. Triangle AOD is rectangular since AC and BD are perpendicular.
DО = √ АD² – AO² (by the Pythagorean theorem).
AO = 1/2 AC = 10: 2 = 5 cm.
The length of each side of the rhombus = P: 4 = 52: 4 = 13 cm AD = 13 cm.
DO = √13² – 5² = √169 – 25 = √144 = 12 cm.
Diagonal ВD = 12 х 2 = 24 cm.
Answer: BD diagonal is 24 cm.
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