Question

A triangle has sides 42, 4x, and 2x−6. What is the possible range of x?

? < x < ?

Answer 1

`8\ units< x < 18\ units`

Explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Applying the Theorem

case 1)
`42+4x > 2x-6`

`4x-2x > -6-42`

`2x > -48`

`x > -24\ units`

case 2)
`42+(2x-6) >4x`

`42-6 >4x-2x`

`36 >2x`

`18 >x` -----> rewrite

`x<18\ units`

case 3)
`4x+(2x-6) > 42`

`4x+2x > 42+6`

`6x > 48`

`x > 8\ units`

therefore

`8\ units< x < 18\ units`