The diagonals of the rhombus are 10 and 24. Find the side of the rhombus.

univerkov | August 5, 2021 | education

The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.

Then ОВ = ОД = ВD / 2 = 10/2 = 5 cm, AO = СО = АС / 2 = 24/2 = 12 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 = AO ^ 2 + OB ^ 2 = 144 + 25 = 169.

AB = 13 cm.

Since the lengths of all sides of a rhombus are equal, then BC = CD = AD = AB = 13 cm.

Answer: The length of the side of the rhombus is 13 cm.

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