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# help

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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.

May 22, 2020

#1
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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)

May 22, 2020
#2
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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

May 23, 2020