# The height AH of the rhombus ABCD Divides the side CD into segments DH = 21 and CH

October 4, 2021 | education

| **The height AH of the rhombus ABCD Divides the side CD into segments DH = 21 and CH = 8 find the height of the rhombus.**

Determine the length of the side of the rhombus CD.

CD = DH + CH = 21 + 8 = 29 cm.

Since the lengths of all its sides are equal for a rhombus, AD = AB = CD = CB = 29 cm.

The triangle ADH is rectangular, since AH is the height of the rhombus, then, by the Pythagorean theorem,

AH ^ 2 = AD ^ 2 – DH ^ 2 = 29 ^ 2 – 21 ^ 2 = 841 – 441 = 400.

AH = 20 cm.

Answer: The height of the rhombus is 20 cm.

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