Difference between revisions of "1996 AHSME Problems/Problem 28"

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==Problem 28==
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On a <math> 4\times 4\times 3 </math> rectangular parallelepiped, vertices <math>A</math>, <math>B</math>, and <math>C</math> are adjacent to vertex <math>D</math>. The perpendicular distance from <math>D</math> to the plane containing
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<math>A</math>, <math>B</math>, and <math>C</math> is closest to
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<asy>
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size(120);
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import three;
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currentprojection=orthographic(1, 4/5, 1/3);
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draw(box(O, (4,4,3)));
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triple A=(0,4,3), B=(0,0,0) , C=(4,4,0), D=(0,4,0);
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draw(A--B--C--cycle, linewidth(0.9));
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label("$A$", A, NE);
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label("$B$", B, NW);
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label("$C$", C, S);
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label("$D$", D, E);
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label("$4$", (4,2,0), SW);
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label("$4$", (2,4,0), SE);
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label("$3$", (0, 4, 1.5), E);
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</asy>
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<math> \text{(A)}\ 1.6\qquad\text{(B)}\ 1.9\qquad\text{(C)}\ 2.1\qquad\text{(D)}\ 2.7\qquad\text{(E)}\ 2.9 </math>
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==See also==
 
==See also==
 
{{AHSME box|year=1996|num-b=27|num-a=29}}
 
{{AHSME box|year=1996|num-b=27|num-a=29}}

Revision as of 13:30, 19 August 2011

Problem 28

On a $4\times 4\times 3$ rectangular parallelepiped, vertices $A$, $B$, and $C$ are adjacent to vertex $D$. The perpendicular distance from $D$ to the plane containing $A$, $B$, and $C$ is closest to

[asy] size(120); import three; currentprojection=orthographic(1, 4/5, 1/3); draw(box(O, (4,4,3))); triple A=(0,4,3), B=(0,0,0) , C=(4,4,0), D=(0,4,0); draw(A--B--C--cycle, linewidth(0.9)); label("$A$", A, NE); label("$B$", B, NW); label("$C$", C, S); label("$D$", D, E); label("$4$", (4,2,0), SW); label("$4$", (2,4,0), SE); label("$3$", (0, 4, 1.5), E); [/asy]

$\text{(A)}\ 1.6\qquad\text{(B)}\ 1.9\qquad\text{(C)}\ 2.1\qquad\text{(D)}\ 2.7\qquad\text{(E)}\ 2.9$

See also

1996 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 27
Followed by
Problem 29
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