robycarroll2005 robycarroll2005
  • 23-07-2018
  • Mathematics
contestada

Two sides of a triangle have lengths of 16 cm and 17 cm. Which could be the length of the third side?

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gmany
gmany gmany
  • 24-07-2018

The sum of the lengths of any two sides of a triangle must be greater than to the length of the third side.


x - third side


if x ≤ 16 < 17 or 16 ≤ x < 17 then


x + 16 > 17 |-16

x > 1


x ∈ (1; 16]


if 16 < 17 ≤ x then


16 + 17 > x

33 > x


x ∈ [17; 33)


Answer: x ∈ (1; 16] ∪ [17; 33) → 1 < x ≤ 16 or 17 ≤ x < 33

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