A rectangular box is 4 cm thick, and its square bases measure 16 cm by 16 cm. What is the distance, in centimeters, from the center point P of one square base to corner Q of the opposite base? Express your answer in simplest terms.
The center of the base is the point where the diagonals intersect.
First, let's find the length of the diagonal.
Draw in one diagonal; this will give us a right triangle whose hypotenuse is the diagonal,
and whose sides are the sides of the box.
We can use the Pythagorean Theorem: c2 = a2 + b2 ---> c2 = 162 + 162
c2 = 256 + 256 = 512 ---> c = sqrt(512) = 16
To find he distance from the center of the base to a corner of the opposite base:
draw a right triangle from the center of the base to a corner of the base then up the side.
From the center of the base to a corner of the base is one-half of a diagonal = 8.
Up the side is 4.
We can again use the Pythagoren theorem with one side = 8, the other side = 4, and we
need to find the hypotenuse: c2 = a2 + b2 ---> c2 = 82 + 42 = 64 + 16 = 80
---> c = sqrt(80)