In parallelogram ABCD AB = 4 cm, AD = 5√2 cm, angle A = 45 degrees. Find the diagonals of the parallelogram.

univerkov | April 9, 2021 | education

To determine the lengths of the diagonals, we will use the cosine theorem for a triangle.

BD ^ 2 = AB ^ 2 + AD ^ 2 – 2 * AB * AD * Cos45.

ВD ^ 2 = 16 + 50 – 2 * 4 * 5 * √2 * √2 / 2 = 66 – 40 = 26.

ВD = √26 cm.

The sum of the adjacent angles of the parallelogram is 180, then the angle ADC = 180 – BAD = 180 – 45 = 135.

Then: AC ^ 2 = AD ^ 2 + CD ^ 2 – 2 * AD * CD * Cos135.

AC ^ 2 = 50 + 16 – 2 * 5 * √2 * 4 * (-√2 / 2) = 66 + 40 = 106.

AC = √106 cm.

Answer: The diagonals of the parallelogram are √26 cm and √106 cm.

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