The lengths of the diagonals of the rhombus ABCD are 14 cm and 48 cm. Find the perimeter of the rhombus ABCD.
| March 3, 2021 | education
The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.
Then AO = CO = AC / 2 = 48/2 = 24 cm, BO = DO = BD / 2 = 14/2 = 7 cm.
The ABO triangle is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse AB. AB ^ 2 = AO ^ 2 + BO ^ 2 = 576 + 49 = 625.
AB = 25 cm.
In a rhombus, the lengths of all sides are equal, then Ravsd = AB * 4 = 25 * 4 = 100 cm.
Answer: The perimeter of the rhombus is 100 cm.
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