Question

In Euclidean geometry, the sum of the lengths of 2 sides of a triangle is greater than the length of the third side. The lengths of 3 sides of a triangle are 3x, 7, and 12.

Answer 1

Answer:
`x \in ((5)/(3),(19)/(3))`

Explanation:

Given

length of three sides are

`3x, 7\ and\ 12`

according to Euclidean geometry

`7+12>3x`

`19>3x`

`(19)/(3)>x`

also

`3x+7>12`

`3x>5`

`x>(5)/(3)`

therefore value of
`x \in ((5)/(3),(19)/(3))`

If x is an integer then x can be
`2,3,4,5,6`