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16 June, 02:37

The lengths of two sides of a triangle are 3 inches in 8 inches find the range of possible links for the third side S

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  1. 16 June, 04:33
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    If a, b and c are the lengths of the sides of a triangle then

    if a ≤ b ≤ c, then a + b > c.

    1. a ≤ 3 ≤ 8 then a + 3 > 8 → a > 8 - 3 → a > 5 FALSE, because a ≤ 3.

    2. 3 ≤ a ≤ 8 then 3 + a > 8 → a > 5 therefore 5 < a ≤ 8

    3. 3 ≤ 8 ≤ a then 3 + 8 > a → 11 > a → a < 11 therefore 8 ≤ a < 11.

    Answer: 5 < a < 11 → S = (5, 11)
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