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14 June, 21:30

Which three lengths could be the lengths of the sides of a triangle? Question 23 options: 21 cm, 7 cm, 6 cm 12 cm, 5 cm, 17 cm 9 cm, 22 cm, 11 cm 10 cm, 15 cm, 24 cm

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  1. 14 June, 23:30
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    Answer: option d is the correct answer

    Step-by-step explanation:

    Looking at the different lengths given,

    It is only the the last set containing

    10 cm, 15 cm, 24 cm that can be the sides of a triangle.

    This can be proven by finding the area of the triangle with the sides given. Considering

    10 cm, 15 cm, 24 cm

    Perimeter = 10+15+24 = 49

    Semi perimeter, s = 49/2 = 24.5

    Area = √s (s-a) (s-b) (s-c) = √24.5 (24.5-10) (24.5-15) (24.5-24) = √24.5 * 14.5 * 9.5 * 0.5 = √1687.4375 = 41.07843108007

    If we try finding the area for the other given lengths,

    Considering

    1) 21 cm, 7 cm, 6 cm

    s = 17

    Looking for the area like we just did will lead to square root of a negative number (17-24 = - 7) and the area cannot be determined.

    2) 12 cm, 5 cm, 17 cm

    s = 17

    Looking for the area like we did previously, the area will be zero (17-17 = 0) and this is impossible.

    3) 9 cm, 22 cm, 11 cm

    s = 21

    Looking for the area like we did previously will lead to square root of a negative number (21-22 = - 1) and the area cannot be determined.

    In conclusion, the three lengths that could be the lengths of the sides of a triangle are 10 cm, 15 cm, 24 cm
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