ONE
    Númas
    ← Back to the programme
    OlympiadMediumCombinatorics7–9

    How many different triangles with whole-number side lengths have perimeter 1212? Triangles with the same three lengths count once.

    Quantos triângulos diferentes com lados de comprimento inteiro têm perímetro 1212? Triângulos com os mesmos três comprimentos contam uma só vez.

    Answer options

    Solution

    Step 1 of 3

    1. 1.List the triples a≤b≤ca \le b \le c with a+b+c=12a + b + c = 12: (1,1,10),(1,2,9),(1,3,8),(1,4,7),(1,5,6),(2,2,8),(2,3,7),(2,4,6),(2,5,5),(3,3,6),(3,4,5),(4,4,4)(1,1,10), (1,2,9), (1,3,8), (1,4,7), (1,5,6), (2,2,8), (2,3,7), (2,4,6), (2,5,5), (3,3,6), (3,4,5), (4,4,4).