In parallelogram ABCD, AB = 4 cm. AD = 5√2 cm. Angle A = 45 °. find the diagonals of the parallelogram.
| September 29, 2021 | education
Since ABCD is a parallelogram, therefore, AD = BC = 5√2 cm.
By the cosine theorem, we find the diagonal BD.
(BD) ^ 2 = (AB) ^ 2 + (AD) ^ 2 – 2 * AB * AD * cosA = (4) ^ 2 + (5√2) ^ 2 – 2 * 4 * 5√2 * cos45º =
= 16 + 50 – 8 * 5 * √2 * √2 / 2 = 26.
BD = √26 cm.
By the cosine theorem, we find the diagonal AC.
(AC) ^ 2 = (AB) ^ 2 + (BC) ^ 2 – 2 * AB * BC * cosB =
= (4) ^ 2 + (5√2) ^ 2 – 2 * 4 * 5√2 * cos (180º – 45º) = 16 + 50 – 8 * 5 * √2 * (- √2 / 2) = 106 …
AC = √106 cm.
Answer: the diagonals of the parallelogram are √26 cm and √106 cm.
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