In a parallelogram, the sides and one of the diagonals are 4cm, 6cm, 7cm

univerkov | September 18, 2021 | education

In a parallelogram, the sides and one of the diagonals are 4cm, 6cm, 7cm, respectively. Find the length of the other diagonal of the parallelogram.

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

AC ^ 2 + BD ^ 2 = 2 * (AD ^ 2 + CD ^ 2).

BD ^ 2 = 2 * (AD ^ 2 + CD ^ 2) – AC ^ 2 = 2 * (36 + 16) – 49 = 104 – 49 = 55.

ВD = √55 cm.

Answer: The length of the other diagonal is √55 cm.

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