In parallelogram ABCD, the diagonals are 5 cm and 7 cm. Calculate the side AB if BC = 2√3 cm.

univerkov | September 11, 2021 | education

1. Diagonal AC = 7 centimeters. Diagonal ВD = 5 centimeters.

2. Using one of the properties of the diagonals of the parallelogram that the total value of the squares of the diagonals is equal to the doubled total value of the squares of the adjacent sides, we calculate the length of the side AB:

AC² + BD² = 2 x (BC² + AB²).

7² + 5² = 2 (2√3) ² + 2AB².

49 + 25 = 24 + 2AB².

AB² = 25.

AB = 5 centimeters.

Answer: the length of the AB side is 5 centimeters.

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