2015 AMC 8

Complete problem set with solutions and individual problem pages

Problem 8 Easy

What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19?

  • A.

    24

  • B.

    29

  • C.

    43

  • D.

    48

  • E.

    57

Answer:D

Solution 1

We know from the Triangle Inequality that the last side, s, fulfills s<5+19=24. Adding 5+19 to both sides of the inequality, we get s+5+19<48, and because s+5+19 is the perimeter of our triangle, \boxed{\textbf{(D)}\ 48} is our answer.

 

Solution 2

s, fulfills s<5+19=24, meaning that s<24. The greatest value of s can be 23. 23+5+19 is 47. 48 is our nearest answer choice so its \boxed{\textbf{(D)}\ 48}.

Related Problems
Problem 6 2015 AMC 8
Problem 7 2015 AMC 8
Problem 9 2015 AMC 8
Problem 10 2015 AMC 8
Think Academy Powered by ChatGPT