Answer:
29.86 units
Step-by-step explanation:
In the triangle BIS, IT is the bisector of angle BIS,
[tex] BI \cong ST.... (given) \\[/tex]
Let BI = ST = x... (1)
By angle bisector property of a triangle, we have:
[tex] \frac{BI}{IS} = \frac{BT}{ST}.... (2)\\\\
\frac{x}{12} = \frac{4}{x}\\\\
x\times x = 12\times 4\\\\
x^2 = 48\\\\
x=\sqrt{48}\\\\
x = 6.92820323\\\\
x = 6.93\\[/tex]
Therefore,
BI = ST =6.93
Perimeter of triangle BIS
= BI + IS + ST + BT
= 6.93 + 12 + 6.93 + 4
= 29.86 units
