Find the diagonal of a rectangular parallelepiped, the sides of the base

Find the diagonal of a rectangular parallelepiped, the sides of the base of which are 2cm and 3cm, and the height of the rectangular parallelepiped is 4cm

1. In geometry, the Pythagorean theorem is known, which says: the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the legs.

2. According to the problem statement, a rectangular parallelepiped with base sides of 3 cm and 2 cm is given.

So we can calculate the diagonal of the base d by the formula:

d² = 3² + 2² = 9 + 4 = 15, whence d = √15 cm.

3. Now you can determine the diagonal D of the parallelepiped from the triangle with legs, which are the given height 4 cm and the found d.

D² = d² + 4² = 15 + 16 = 31 cm; D = √31 cm.

Answer: The diagonal is √31 cm.