Difference between revisions of "1996 AHSME Problems/Problem 28"
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| + | ==Problem 28== | ||
| + | |||
| + | 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 | ||
| + | <math>A</math>, <math>B</math>, and <math>C</math> 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> | ||
| + | |||
| + | <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> | ||
| + | |||
==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 
rectangular parallelepiped, vertices 
, 
, and 
are adjacent to vertex 
. The perpendicular distance from to the plane containing
, , and 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]](http://latex.artofproblemsolving.com/7/0/1/7010c0e675bed9ebff14ddb001a486ffc078df4c.png)
See also
| 1996 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 27 |
Followed by Problem 29 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
