The diagonal of a rectangular parallelepiped is 5√14 cm, and its dimensions are 1: 2: 3.

The diagonal of a rectangular parallelepiped is 5√14 cm, and its dimensions are 1: 2: 3. Find the dimensions of the box.

Let the lengths of the parallelogram measurements be equal to X cm, 2 * X cm, 3 * X cm.

The square of the diagonal of a parallelepiped is equal to the sum of the squares of its three dimensions, then:

(5 * √14) ^ 2 = X ^ 2 + 4 * X ^ 2 + 9 * X ^ 2.

14 * X ^ 2 = 350.

X ^ 2 = 350/14 = 25.

X = 5 cm.

Then AB = 5 cm, AD = 2 * 5 = 10 cm, AA1 = 3 * 5 = 15 cm.

Answer: The dimensions of the parallelepiped are 5 cm, 10 cm, 15 cm.