AMC 8 Daily Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 4 Easy

The side length of a triangle are three consecutive integers. The length of the longest side is \frac{2}{5} of the perimeter of the triangle. What is the length of the longest side?

  • A.

    4

  • B.

    5

  • C.

    6

  • D.

    7

  • E.

    8

Answer:C

Let n, n+1, and n+2 be the lengths of the sides of the triangle. Then the perimeter of the triangle is n+\left( n+1 \right)+\left( n+2 \right)=3n+3. Using the fact that the length of the longest side is \frac25 of the perimeter, it follows that: 0.4\left( 3n +3 \right)=n+2\Rightarrow n=4. The longest side is n+2=4+2=6. Thus, answer \left( \text{C} \right)6 is correct.

Related Problems
Problem 1 AMC 8 Daily Practice Round 3
Problem 2 AMC 8 Daily Practice Round 3
Problem 3 AMC 8 Daily Practice Round 3
Problem 5 AMC 8 Daily Practice Round 3
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