Since the lengths of the sides of the rhombus are equal, then AB = BC = CD = AD = P / 4 = 164/4 = 41 cm.
The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.
Then AO = AC / 2 = 80/2 = 40 cm.
In a right-angled triangle AOB, according to the Pythagorean theorem, we determine the length of the leg OB.
OB ^ 2 = AB ^ 2 – AO ^ 2 = 1681 – 1600 = 81.
ОВ = 9 cm, then ВD = 2 * ОВ = 2 * 9 = 18 cm.
Answer: The length of the smaller diagonal is 18 cm.
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