Find the diagonal AC of the parallelogram ABCD if AB = 16, AD = 7, BD = 21.

univerkov | January 20, 2021 | education

We use the property of the parallelogram, according to which the sum of the squares of the diagonals of the parallelogram is equal to the doubled sum of the squares of its sides.

AC ^ 2 + ВD ^ 2 = 2 * (AB ^ 2 + AD ^ 2).

AC ^ 2 = 2 * (AB ^ 2 + AD ^ 2) – ВD ^ 2 = 2 * (256 + 49) – 441 = 610 – 441 = 169.

AC = 13 cm.

Answer: The length of the AC diagonal is 13 cm.

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