Step 1: State the property of an isosceles triangle
One of the properties of an isosceles triangle that we will apply to get the answer is that an isosceles triangle has two equal sides.
From the triangle ABC given, the equal sides are the sides with signs on them. These lines are line AC and line BC
Step 2: Determine the value of x
To achieve this, we equate the expression of line AC to line BC
[tex]\begin{gathered} AC=3x+9(\text{given)} \\ BC=4x+4(\text{given)} \\ BC=AC \\ 4x+4=3x+9 \\ 4x-3x=9-4 \\ x=5 \end{gathered}[/tex]
Step 3: Determine the value of line AB
In other to determine the value of line AB, we will substitute for x in the expression for line AB
[tex]AB=8x+5(\text{given)}[/tex][tex]\begin{gathered} x=5 \\ AB=8(5)+5 \\ AB=40+5 \\ AB=45 \end{gathered}[/tex]
Hence, the value of line AB is 45 units
