# The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of a triangle are 15 ft and 27 ft. Find the possible lengths of the third side?

## The third side must have a length greater than ? ft and less than ? ft.

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Mar 8, 2018

Possible length of third side is $12 < x < 42 \mathmr{and} x | \left(12 , 42\right)$ ft.

#### Explanation:

15+27=42 ; 27-15=12 . Therefore the third side must be

less than $42$ ft ant greater than $12$ ft. Therefore

possible length of third side of size $x$ is

$12 < x < 42 \mathmr{and} x | \left(12 , 42\right)$ ft [Ans]

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