The sides of the parallelogram are 2√2 cm and 5 cm and one of the corners is 45 degrees.
| May 10, 2021 | education
The sides of the parallelogram are 2√2 cm and 5 cm and one of the corners is 45 degrees. Find the diagonals of the parallelogram.
In triangle ABD, we apply the cosine theorem and determine the length of the diagonal BD.
BD ^ 2 = AB ^ 2 + AD ^ 2 – 2 * AB * AD * Cos45 = 8 + 25 – 2 * 2 * √2 * 5 * √2 / 2 = 33 – 20 = 13.
ВD = √13 cm.
In a parallelogram, the sum of adjacent angles is 180, then the angle ABC = (180 – 45) = 135.
In the triangle ABC, we apply the cosine theorem and determine the length of the diagonal AC.
AC2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos135 = 8 + 25 – 2 * 2 * √2 * 5 * (-√2 / 2) = 33 + 20 = 53.
AC = √53 cm.
Answer: The lengths of the diagonals are √13 cm and √53 cm.
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