The side of the rhombus is 41 cm, and one of its diagonals is 18 cm. Find the second diagonal.

univerkov | February 19, 2021 | education

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

Then AO = OC = AC / 2, ВO = DO = ВD / 2 = 18/2 = 9 cm, and triangle AOB is rectangular.

In a right-angled triangle AOB, according to the Pythagorean theorem, we determine the length of the leg AO.

AO ^ 2 = AB ^ 2 – OB ^ 2 = 1681 – 81 = 1600.

AO = 40 cm.

Then AC = 2 * AO = 2 * 40 = 80 cm.

Answer: The length of the second diagonal is 80 cm.

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