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Question

A rectangular box is 8 cm thick, and its square bases measure 32 cm by 32 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.

Accepted Answer

Let A be the corner of the box shown, directly above point Q: FIGURE Since PA is half a diagonal of the top face, we have PA = 162 cm. From right triangle PAQ, we have PQ = PA^2 + AQ^2 = 512+64 = 24 cm.