## Leg of Isosceles Triangle

The length of each leg of an isosceles triangle is $x+1$, and the length of the base is $3x-2$. Determine all possible real values of $x$.
Source: NCTM Mathematics Teacher 2006

SOLUTION

For $ABC$ to be a triangle (Triangle Inequality Theorem)
$CA+AB>BC$
$x+1+x+1>3x-2$
$2x+2>3x-2$
$4>x$
Also, length $BC$ must be positive
$3x-2>0$
$3x>2$
$x>2/3$
All real possible values of $x$ are
$2/3

Answer: $2/3