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.
+23246 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)
+36916 From a corner to the center of the opposite side is 8 for x 8 for y and 4 for z
sqrt (8^2 + 8^2 + 4^2 ) = sqrt 144 = 12 cm
