which set if side lengths can form a traingle ? A . 6, 8, an 16 centimeters B. 6, 8, and 10 centimeters C. 6, 7, and 14 centimeters D . 6,7,

Question

which set if side lengths can form a traingle ? A . 6, 8, an 16 centimeters B. 6, 8, and 10 centimeters C. 6, 7, and 14 centimeters D . 6,7, and 20 centimeters​

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Remi 1 month 2021-09-08T16:37:55+00:00 1 Answer 0

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    2021-09-08T16:39:07+00:00

    Option b  – 6, 8, and 10 centimeters  can form a triangle

    Step-by-step explanation:

    Step 1 :

    Three lengths can be the sides of triangle if the 2 length’s sum is always  greater than length of third side. This should be true for all 3 combinations.

    If p,q,r are 3 lengths then this will forma triangle if

    p + q > r

    q + r > p

    p + r > q

    Step 2 :

    a)

    p = 6, q = 8, r = 16

    p + q = 6 + 8 = 14

    This is not greater than r = 16.

    So these length cannot form a triangle.

    Step 3 :

    b)

    p = 6, q = 8, r = 10

    p + q = 6 + 8 = 14 . This is greater than r = 10

    q + r = 8 + 10 = 18. This is greater than r = 6

    p + r = 6 + 10 = 16. This is greater than r = 8

    Since all the 3 inequalities are satisfied these lengths can form a triangle

    Step 4 :

    c)

    p = 6, q = 7, r = 14

    p + q = 6 + 7 = 13

    This is not greater than r = 14.

    So these length cannot form a triangle.

    Step 5 :

    d)

    p = 6, q = 7, r =20

    p + q = 6 + 7 = 13

    This is not greater than r = 20.

    So these length cannot form a triangle.

    Step 6 :

    Answer :

    Option b  is the correct answer

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