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<x<4

Answer: 2/3<x<4

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About mvtrinh

Retired high school math teacher.
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