Difference between revisions of "1998 AHSME Problems/Problem 29"
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<math> \mathrm{(A) \ } 4.0 \qquad \mathrm{(B) \ } 4.2 \qquad \mathrm{(C) \ } 4.5 \qquad \mathrm{(D) \ } 5.0 \qquad \mathrm{(E) \ } 5.6</math> | <math> \mathrm{(A) \ } 4.0 \qquad \mathrm{(B) \ } 4.2 \qquad \mathrm{(C) \ } 4.5 \qquad \mathrm{(D) \ } 5.0 \qquad \mathrm{(E) \ } 5.6</math> | ||
+ | |||
+ | |||
+ | == Solution == | ||
+ | <asy> | ||
+ | real e = 0.1; | ||
+ | |||
+ | dot((0,-1)); | ||
+ | dot((1,-1)); | ||
+ | dot((-1,0)); | ||
+ | dot((0,0)); | ||
+ | dot((1,0)); | ||
+ | dot((2,0)); | ||
+ | dot((-1,1)); | ||
+ | dot((0,1)); | ||
+ | dot((1,1)); | ||
+ | dot((0,2)); | ||
+ | dot((-1,-1)); | ||
+ | dot((2,2)); | ||
+ | dot((1,2)); | ||
+ | dot((2,1)); | ||
+ | dot((2,-1)); | ||
+ | dot((-1,2)); | ||
+ | draw((0.8, -1.4+e)--(1.8-e, 0.6)--(-0.2, 1.6-e)--(-1.2+e, -0.4)--cycle); | ||
+ | </asy> | ||
+ | The best square's side length is slightly less than <math>\sqrt 5</math>, yielding an answer of <math>\boxed{\textbf{(D) }5.0}</math> | ||
== See also == | == See also == | ||
{{AHSME box|year=1998|num-b=28|num-a=30}} | {{AHSME box|year=1998|num-b=28|num-a=30}} | ||
+ | {{MAA Notice}} |
Latest revision as of 00:54, 30 January 2019
Problem
A point in the plane is called a lattice point if both and are integers. The area of the largest square that contains exactly three lattice points in its interior is closest to
Solution
The best square's side length is slightly less than , yielding an answer of
See also
1998 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 28 |
Followed by Problem 30 | |
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 |
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