The base of the rectangular parallelepiped is a square; the diagonal of a parallelepiped is 2√6 cm
| June 9, 2021 | education
The base of the rectangular parallelepiped is a square; the diagonal of a parallelepiped is 2√6 cm, and its measurements are related as 1: 1: 2. Find the dimensions of a parallelepiped
Let the length of the side of the square at the base of the parallelepiped be X cm, AB = BC = CD = AD = X cm, then the height of the prism AA1 = 2 * X cm.
In the square ABCD, construct the diagonal AC and determine its length.
AC ^ 2 = AD ^ 2 + CD ^ 2 = X ^ 2 + X ^ 2 = 2 * X ^ 2.
AC = X * √2 cm.
In a right-angled triangle ACA1, according to the Pythagorean theorem, CA1 ^ 2 = AC ^ 2 + AA1 ^ 2.
24 = 2 * X ^ 2 + 4 * X ^ 2 = 6 * X ^ 2.
X ^ 2 = 24/6 = 4.
X = AB = BC = CD = AD = 2 cm.
AA1 = 4 cm.
Answer: The dimensions of the parallelepiped are 2 cm, 2 cm, 4 cm.
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