The sides of the parallelogram are 7 cm and 9 cm, and the diagonals are 4: 7. find the diagonals of the parallelogram
| August 17, 2021 | education
Let the length of the diagonal BD = 4 * X, then the diagonal AC = 7 * X cm.
The diagonals of the parallelogram, at the point of their intersection, are divided in half, then OB = BD / 2 = 2 * X cm.
In triangle ABC, segment BO is its median, since point O divides AC in half.
According to the formula for the median of a triangle:
BO ^ 2 = (2 * AB ^ 2 + 2 * BC ^ 2 – AC ^ 2) / 4.
4 * X ^ 2 = (98 + 162 – 49 * X ^ 2) / 4.
16 * X ^ 2 + 49 * X ^ 2 = 260.
X ^ 2 = 260/65 = 4.
X = 2.
BD = 2 * 4 = 8 cm, AD = 2 * 7 = 14 cm.
Answer: The diagonals of the parallelogram are 8 cm and 14 cm.
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