We were given the following information:
LT = 12
GL = 13
GR = x - 3
The incenter of a triangle refers to the intersection point of all interior angle bisectors of the triangle. The incenter is equidistant to the sides, they are all the same
If triangle JKL has G as its incenter, the following will be found to be true:
[tex]|GR|\cong|GS|\cong|GT|[/tex]
However, we were not given any of the above distances GR, GS & GT. We can obtain GT by using the Pythagoras Theorem on the triangle GTL as shown below:
[tex]\begin{gathered} |GT|^2=|GL|^2-|LT|^2 \\ |GT|^2=13^2-12^2 \\ |GT|^2=169-144 \\ |GT|^2=25 \\ \text{Take the square root of both sides, we have:} \\ |GT|=\sqrt[]{25} \\ |GT|=5 \\ \\ \therefore|GT|=5 \end{gathered}[/tex]
Since GT equals 5, it implies that GS & GT will also equal 5
We will obtain the value of ''x'' as shown below:
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