1992 AJHSME Problems/Problem 17

Problem

The sides of a triangle have lengths $6.5$ , $10$ , and $s$ , where $s$ is a whole number. What is the smallest possible value of $s$ ?

$[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]$

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 7$

Solution

By Triangle Inequality, $6.5 + s >10$ and therefore $s>3.5$ . The smallest whole number that satisfies this is $\boxed{\text{(B)}\ 4}$ .

1992 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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1992 AJHSME Problems/Problem 17

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