The side of the rhombus is 6, and one of its diagonals is equal to 4 roots of 5. Find the length of the second diagonal.

univerkov | July 19, 2021 | education

The diagonals of the rhombus, at the point of their intersection, are divided in half and intersect at right angles, then BO = BD / 2 = 4 * √5 / 2 = 2 * √5 cm, and the triangle AOB is rectangular.

By the Pythagorean theorem, in the right-angled triangle AOB, we determine the length of the leg AO.

AO ^ 2 = AB ^ 2 – BO ^ 2 = 36 – 20 = 16.

AO = 4 cm.

Then AC = 4 * 2 = 8 cm.

Answer: The length of the second diagonal is 8 cm.

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