Difference between revisions of "1992 AJHSME Problems/Problem 17"
Mrdavid445 (talk | contribs) (Created page with "==Problem== The sides of a triangle have lengths <math>6.5</math>, <math>10</math>, and <math>s</math>, where <math>s</math> is a whole number. What is the smallest possible va...") |
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<math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 7</math> | <math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 7</math> | ||
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| + | ==Solution== | ||
| + | By [[Triangle Inequality]], <math>6.5 + s >10</math> and therefore <math>s>3.5</math>. The smallest whole number that satisfies this is <math>\boxed{\text{(B)}\ 4}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1992|num-b=16|num-a=18}} | ||
Revision as of 21:47, 22 December 2012
Problem
The sides of a triangle have lengths 
, 
, and 
, where is a whole number. What is the smallest possible value of ?
![[asy] pair A,B,C; A=origin; B=(10,0); C=6.5*dir(15); dot(A); dot(B); dot(C); draw(B--A--C); draw(B--C,dashed); label("$6.5$",3.25*dir(15),NNW); label("$10$",(5,0),S); label("$s$",(8,1),NE); [/asy]](http://latex.artofproblemsolving.com/c/9/2/c92ca742ef1e1c4b45c953991f78ff1e6bc82f1a.png)
Solution
By Triangle Inequality, 
and therefore 
. The smallest whole number that satisfies this is 
.
See Also
| 1992 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
