Difference between revisions of "2015 AMC 8 Problems/Problem 8"
Math101010 (talk | contribs) |
|||
Line 3: | Line 3: | ||
<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>c</math>, fulfills <math>c<5+19=24</math>. Adding <math>5+19</math> to both sides of the inequality, we get <math>c+5+19<48</math>. However, we know that <math>c+5+19</math> is the perimeter of our triangle, so we get <math>\boxed{\textbf{(D) }~48}</math> as our answer. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2015|num-b=7|num-a=9}} | {{AMC8 box|year=2015|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 18:33, 25 November 2015
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 . However, we know that is the perimeter of our triangle, so we get as 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.