Maths

the points A,B,C and D lie on a straight line. The ratio of the length of AB to the length of BC is 3:4 and the ratio of the length of AC to the length of CD is 2:1. Find the ratio of the length of BC to the length of AD ?

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  1. AC = AB+BC = 3+4 = 7
    AC/CD = 2/1, so CD = 7/2

    AD = AC+CD, so
    BC/AD = 4/(7 + 7/2) = 8/21

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  2. AB:BC=3:4, so AC=AB+BC=3+4=7;
    AC:CD=2:1, so AC=2;

    because we get 2 different length for AC, we change the given ratio AC:CD into an equivalent one where AC=7 as follows: AC:CD = 2 : 1 = 7 : 3.5 (multiply both sides by 3.5)

    Now we have AC:CD = 7 : 3.5 and AD = AC+CD= 7+3.5 = 10.5

    and the answer is: the ratio of BC:AD = 4: 10.5

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  3. AB:BC=3:4, so AC=AB+BC=3+4=7;
    AC:CD=2:1, so AC=2;

    because we get 2 different length for AC, we change the given ratio AC:CD into an equivalent one where AC=7 as follows: AC:CD = 2 : 1 = 7 : 3.5 (multiply both sides by 3.5)

    Now we have AC:CD = 7 : 3.5 and AD = AC+CD= 7+3.5 = 10.5

    and the answer is: the ratio of BC:AD = 4: 10.5

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