The lengths of the diagonals of the rhombus are 16 cm and 20 cm. Find the perimeter of the rhombus.
May 21, 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 = 20/2 = 10 cm, BO = DO = BD / 2 = 16/2 = 8 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 = 100 + 64 = 164.
AB = 2 * √41 cm.
In a rhombus, the lengths of all sides are equal, then Ravsd = AB * 4 = 2 * √42 * 4 = 8 * √41 cm.
Answer: The perimeter of the rhombus is 8 * √41 cm.
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