How to find the sides of a rhombus if the diagonals of 16cm and 30cm are known?
| May 25, 2021 | education
The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles. Then ОВ = ОD = ВD / 2 = 16/2 = 8 cm, AO = OC = АС / 2 = 30/2 = 15 cm, and the triangle AOB is rectangular.
By the Pythagorean theorem, in the right-angled triangle AOB, we determine the length of the hypotenuse AB.
AB ^ 2 = OA ^ 2 + OB ^ 2 = 225 + 64 = 289.
AB = 17 cm.
In a rhombus, the lengths of the sides are equal, BC = CD = AD = AB = 17 cm.
Answer: The length of the side of the rhombus is 10 cm.
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