A rope that is 245cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2/3, and the ratio of the lenghts of the second piece to the third piece is 4/5. What is the length of the longest of the the three pieces?


  1. The length of the longest piece of the cut rope is; 105 cm

    How to work with ratios?

    We are given that;
    Length of rope = 245 cm
    We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.
    Multiply 1st ratio by 4 and 2nd ratio by 3:
    Now, the ratio becomes: 8:12 and 12:15
    And the ratio of three pieces can be represented as:
    8: 12: 15, this ratio is the first piece: second piece: third piece
    8x + 12x + 15x = 245
    35x = 245
    x = 245/35
    So, the pieces lengths will be;
    First piece = 8 * 7 = 56 cm
    Second piece = 12 * 7 = 84 cm
    Third piece = 15 * 7 = 105 cm
    Read more about ratios at;


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