JC10idn
Answered

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How to know if the lengths may form a triangle? For example. I have 3 cm, 10 cm, 15 cm sticks, will it form a triangle? How to guess/predict just with the
info's about the lengths? not by trying it in actual.

Sagot :

Since triangle or trigon has three sides, let:

a = side 1
b = side 2
c = side 3

If a and b are the two sides, then, to form a triangle the third side must satisfy the condition:
(a - b ) < c < a + b

Side c must be greater than the difference of sides a and b, but less than the sum of a  and b.

Given:
Option 1:
Side a = 3 cm
Side b = 10 cm
Side c = 15 cm

(10-3) < 15 < (3+ 10)
        7 < 15 < 13       ⇒    False
                                  ⇒   The third side must be
                                        {8, 9, 10, 11, 12}, 
                                         not {15}

Option 2:
Side a = 10 cm
Side b = 15 cm
Side c = 3 cm

(15-10) < 3 < (10 + 15)
      5     < 3 <   25   ⇒   False
                               ⇒   The third side must be
                                      {6, 7, 8, 9, 10, ..., 23, 24, 25},
                                      not {3}

Option 3:
Side a = 15 cm
Side b = 3 cm
Side c = 10 cm

(15-3) < 10 < (15 + 3)
     12   < 10 < 18       ⇒   False
                                  ⇒   The third side must be
                                         {13, 14, 15, 16, 17}
                                         not {10}