The sides of the base of the rectangular box are 2 and 3, and its diagonal is 7. Find the height of the box.

In a rectangular parellepiped, all its dimensions (length (a), width (b) and height (h)) are connected by the formula:

d ^ 2 = a ^ 2 + b ^ 2 + c ^ 2, where d is the diagonal of the parallelepiped.

Let’s substitute the data from the task: the sides of the base are equal to 2 and 3, which means a = 2, b = 3 (or vice versa, it is not important here), d = 7. We obtain an equation with variable h.

7 ^ 2 = 2 ^ 2 + 3 ^ 2 + h ^ 2;

49 = 4 + 9 + h ^ 2;

49 = 13 + h ^ 2;

49 – 13 = h ^ 2;

36 = h ^ 2;

h = 6.

Answer: 6.