The base of an rectangular parallelepiped is square of 10 cm side . If the length of the diagonal of parallelepiped is 15 cm . Find its h?

Let x be the height of the parallelepiped.

We're looking for the length of the diagonal

from one vertex to the diagonally opposite

vertex. Next, draw a diagram! You'll see that

the diagonal is the hypotenuse of a right triangle

whose legs are 10√2 and x, and whose hypotenuse

is 15. And so, by Pythagoras, we have

(10√2)^2 + x^2 = 15^2, or

200 + x^2 = 225

x^2 = 25, so the positive solution

is x = 5 cm.