The lengths of the third side must be greater than 10 , but less than 30.
This theorem states that the sum of any two sides of a triangle must be greater than the third side.
The given two sides of triangle is 10 and 20.
Let x be the third side of the triangle.
Now the sum of the given two sides
10 + 20 = 30
Now,according to triangle inequality theorem
x < sum of other two sides
⇒ x < 30
Now Since two sides are 10 and 20 and third side is x.
and we know that x < 30
Let third side be the smallest side.
then x ≤ 10
⇒ x + 10 > 20
⇒ x > 10.
Hence,The lengths of the third side must be greater than 10, but less than 30.
More about triangle inequality theorem :
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