Question

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

Answer 1

Answer:

$8\ units< x < 18\ units$

Step-by-step 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

$x$

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

$4x+2x > 42+6$

$6x > 48$

$x > 8\ units$

therefore

$8\ units< x < 18\ units$