Difference between revisions of "1990 AIME Problems/Problem 14"
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== Problem == | == Problem == | ||
+ | The rectangle <math>ABCD^{}_{}</math> below has dimensions <math>AB^{}_{} = 12 \sqrt{3}</math> and <math>BC^{}_{} = 13 \sqrt{3}</math>. Diagonals <math>\overline{AC}</math> and <math>\overline{BD}</math> intersect at <math>P^{}_{}</math>. If triangle <math>ABP^{}_{}</math> is cut out and removed, edges <math>\overline{AP}</math> and <math>\overline{BP}</math> are joined, and the figure is then creased along segments <math>\overline{CP}</math> and <math>\overline{DP}</math>, we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid. | ||
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+ | [[Image:AIME_1990_Problem_14.png]] | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
− | + | {{AIME box|year=1990|num-b=13|num-a=15}} |
Revision as of 01:46, 2 March 2007
Problem
The rectangle below has dimensions and . Diagonals and intersect at . If triangle is cut out and removed, edges and are joined, and the figure is then creased along segments and , we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid.
Solution
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See also
1990 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |