The perimeter of the rhombus is 20 cm, and one of its diagonals is 8 cm. Find the second diagonal of the rhombus.
| June 15, 2021 | education
A rhombus is a parallelogram in which all sides are equal.
Because P = 20 cm, then AB = BC = CD = AD = 5 cm.
The diagonals of the rhombus are perpendicular to each other and the intersection point is halved.
Thus, BO = OD = 4 cm and AO = OC.
∆ABO – rectangular. By the Pythagorean theorem, we have AB ^ 2 = AO ^ 2 + BO ^ 2 or AO = √ (AB ^ 2 – BO ^ 2) = √ (5 ^ 2 – 4 ^ 2) = √9 = 3 cm.
Since AO = OC = 3cm, AC = 6cm.
Answer: AC = 6 cm.
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