Difference between revisions of "2000 AMC 10 Problems/Problem 7"
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==Problem== | ==Problem== | ||
+ | |||
+ | In rectangle <math>ABCD</math>, <math>AD=1</math>, <math>P</math> is on <math>\overline{AB}</math>, and <math>\overline{DB}</math> and <math>\overline{DP}</math> trisect <math>\angle ADC</math>. What is the perimeter of <math>\triangle BDP</math>? | ||
+ | |||
+ | <asy> | ||
+ | draw((0,2)--(3.4,2)--(3.4,0)--(0,0)--cycle); | ||
+ | draw((0,0)--(1.3,2)); | ||
+ | draw((0,0)--(3.4,2)); | ||
+ | dot((0,0)); | ||
+ | dot((0,2)); | ||
+ | dot((3.4,2)); | ||
+ | dot((3.4,0)); | ||
+ | dot((1.3,2)); | ||
+ | label("$A$",(0,2),NW); | ||
+ | label("$B$",(3.4,2),NE); | ||
+ | label("$C$",(3.4,0),SE); | ||
+ | label("$D$",(0,0),SW); | ||
+ | label("$P$",(1.3,2),N); | ||
+ | </asy> | ||
+ | |||
+ | <math>\mathrm{(A)}\ 3+\frac{\sqrt{3}}{3} \qquad\mathrm{(B)}\ 2+\frac{4\sqrt{3}}{3} \qquad\mathrm{(C)}\ 2+2\sqrt{2} \qquad\mathrm{(D)}\ \frac{3+3\sqrt{5}}{2} \qquad\mathrm{(E)}\ 2+\frac{5\sqrt{3}}{3}</math> | ||
==Solution== | ==Solution== |
Revision as of 21:44, 8 January 2009
Problem
In rectangle , , is on , and and trisect . What is the perimeter of ?
Solution
.
Since is trisected, .
Thus,
.
Adding, .
See Also
2000 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 | ||
All AMC 10 Problems and Solutions |