Question

I is the incenter of the triangle,AI-3x+7, BI-5x-11, & CI-52-2xBсAI=[ ? ]

Answer 1

We know that the incenter is equidistant from the side, this imply that

$\begin{gathered} AI=BI=C= \\ 3x+7=5x-11=52-2x \end{gathered}$

From the 1st and 2nd equation, we get

$\begin{gathered} 3x+7=5x-11 \\ 7+11=5x-3x \\ 18=2x \\ \text{then} \\ x=\frac{18}{2} \\ x=9 \end{gathered}$

Now, we can substitute this values into AI and get

$\begin{gathered} AI=3x+7 \\ AI=3(9)+7 \\ AI=34 \end{gathered}$

then, the answer is AI= 34 units