A rectangular box of height 10 has a base with edges of length 10. What is the length of a diagonal of this box?

The diagonal of the box is

Step-by-step explanation:

Let

d ----> the diagonal of the base

D ---> the diagonal of the box

step 1

Find the diagonal of the base

Applying the Pythagorean Theorem

step 2

Find the diagonal of the box

In this part the legs of the right triangle are the height of the box and the diagonal of the base

so

Applying the Pythagorean Theorem

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)