2010 AMC 8 Problems/Problem 13
Problem
The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is of the perimeter. What is the length of the longest side?
Solution 1(algebra solution)
Let , , and be the lengths of the sides of the triangle. Then the perimeter of the triangle is . Using the fact that the length of the smallest side is of the perimeter, it follows that:
. The longest side is then . Thus, answer choice is correct.
Solution 2
Since the length of the shortest side is a whole number and is equal to of the perimeter, it follows that the perimeter must be a multiple of . Adding the two previous integers to each answer choice, we see that . Thus, answer choice is correct.
Video by MathTalks
https://www.youtube.com/watch?v=6hRHZxSieKc
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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