Find the side of the rhombus if its diagonals are 6 cm and 8 cm.

univerkov | June 15, 2021 | education

A rhombus is a parallelogram in which all sides are equal: AB = BC = CD = AD.

The diagonals of the rhombus are perpendicular to each other and the intersection point is halved.

Thus, BO = OD = 4 cm and AO = OC = 3 cm.

∆ABO – rectangular. By the Pythagorean theorem, we have AB ^ 2 = AO ^ 2 + BO ^ 2 or AB = √ (AO ^ 2 + BO ^ 2) = √ (4 ^ 2 + 3 ^ 2) = √25 = 5 cm.

Answer: AB = BC = CD = AD = 5 cm.

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