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MATH / A rectangular box is 4 cm thick, and its square bases measure 16 cm by 16 cm.…

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problem

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 PP of one square base to corner QQ of the opposite base? Express your answer in simplest terms. [asy] import three; draw((0,0,1/4)--(1,0,1/4)--(1,1,1/4)--(0,1,1/4)--(0,0,1/4)--cycle,linewidth(2)); draw((0,1,0)--(1,1,0),linewidth(2)); draw((1,1,0)--(1,0,0),linewidth(2)); draw((0,1,0)--(0,1,1/4),linewidth(2)); draw((1,1,0)--(1,1,1/4),linewidth(2)); draw((1,0,0)--(1,0,1/4),linewidth(2)); dot((1/2,1/2,1/4)); dot((0,1,0)); label("PP",(1/2,1/2,1/4),W); label("QQ",(0,1,0),E); [/asy]
Plain-text mathematical notation (without MathML)
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.

[asy]
import three;
draw((0,0,1/4)--(1,0,1/4)--(1,1,1/4)--(0,1,1/4)--(0,0,1/4)--cycle,linewidth(2));

draw((0,1,0)--(1,1,0),linewidth(2));
draw((1,1,0)--(1,0,0),linewidth(2));
draw((0,1,0)--(0,1,1/4),linewidth(2));
draw((1,1,0)--(1,1,1/4),linewidth(2));
draw((1,0,0)--(1,0,1/4),linewidth(2));

dot((1/2,1/2,1/4));
dot((0,1,0));

label("P",(1/2,1/2,1/4),W);
label("Q",(0,1,0),E);
[/asy]
Original LaTeX notation
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.

[asy]
import three;
draw((0,0,1/4)--(1,0,1/4)--(1,1,1/4)--(0,1,1/4)--(0,0,1/4)--cycle,linewidth(2));

draw((0,1,0)--(1,1,0),linewidth(2));
draw((1,1,0)--(1,0,0),linewidth(2));
draw((0,1,0)--(0,1,1/4),linewidth(2));
draw((1,1,0)--(1,1,1/4),linewidth(2));
draw((1,0,0)--(1,0,1/4),linewidth(2));

dot((1/2,1/2,1/4));
dot((0,1,0));

label("$P$",(1/2,1/2,1/4),W);
label("$Q$",(0,1,0),E);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
f43d1f2d-7104-5b7e-941e-56296a293d2e
task_key
geometry--test--f43d1f2d-7104-5b7e-941e-56296a293d2e
task_revision_id
1
config / split
geometry / test

Official source

initial import