Maths-
General
Easy

Question

Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
5 inches, 12 inches

The correct answer is: Hence, all numbers between 7 and 17 will be the length of third side.


    Answer:
    • Hints:
      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • while finding possible lengths of third side use below formula
    difference of two side < third side < sum of two sides

    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.

      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17

      • Step 2:
    difference of two side < third side < sum of two sides
    b – a < c < a + b
    12 – 5 < c < 5 + 12
    7 < c < 17
    Hence, all numbers between 7 and 17 will be the length of third side.
    • Final Answer: 
    Hence, all numbers between 7 and 17 will be the length of third side.

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