In a rectangular parallelepiped, the sides of the base are 24 and 7, and the height is 6√6

In a rectangular parallelepiped, the sides of the base are 24 and 7, and the height is 6√6, find the diagonal of the parallelepiped?

We find the diagonal of a parallelepiped as the hypotenuse of a rectangular triangle, in which the legs are the height of the parallelepiped and the diagonal of the base.

Find the diagonal of the base from, again, the Pythagorean theorem:

x ^ 2 = 24 ^ 2 + 7 ^ 2;

x ^ 2 = 576 + 49;

x ^ 2 = 625;

x = 25.

Found the diagonal of the base, now by the Pythagorean theorem:

d ^ 2 = x ^ 2 + h ^ 2;

d ^ 2 = 25 ^ 2 + (6 ^ (3/2)) ^ 2;

d ^ 2 = 625 + 216;

d ^ 2 = 841;

d = 29.

Answer: The diagonal is 29.