Difference between revisions of "2015 AMC 8 Problems/Problem 8"
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+ | ==Problem== | ||
+ | |||
What is the smallest whole number larger than the perimeter of any triangle with a side of length <math> 5</math> and a side of length <math>19</math>? | What is the smallest whole number larger than the perimeter of any triangle with a side of length <math> 5</math> and a side of length <math>19</math>? | ||
<math>\textbf{(A) }24\qquad\textbf{(B) }29\qquad\textbf{(C) }43\qquad\textbf{(D) }48\qquad \textbf{(E) }57</math> | <math>\textbf{(A) }24\qquad\textbf{(B) }29\qquad\textbf{(C) }43\qquad\textbf{(D) }48\qquad \textbf{(E) }57</math> | ||
+ | ==Solution== | ||
+ | We know from the triangle inequality that the last side, <math>s</math>, fulfills <math>s<5+19=24</math>. Adding <math>5+19</math> to both sides of the inequality, we get <math>s+5+19<48</math>, and because <math>s+5+19</math> is the perimeter of our triangle, <math>\boxed{\textbf{(D)}\ 48}</math> is our answer. | ||
==See Also== | ==See Also== |
Latest revision as of 17:34, 16 January 2021
Problem
What is the smallest whole number larger than the perimeter of any triangle with a side of length and a side of length ?
Solution
We know from the triangle inequality that the last side, , fulfills . Adding to both sides of the inequality, we get , and because is the perimeter of our triangle, is our answer.
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.