Given:
Sides length is:
[tex]\begin{gathered} \text{first side =2}\frac{1}{4}t-5 \\ =\frac{9}{4}t-5 \end{gathered}[/tex][tex]\begin{gathered} 2^{nd}\text{ side=}4t+3 \\ \\ 3^{rd}\text{ side}=\frac{1}{2}t-1 \\ \\ 4^{th}\text{ side=}3t+2 \end{gathered}[/tex]Perimeter of any quadrilateral is:
[tex]\text{Perimeter = first side +2 side +3 side +4 side}[/tex]so perimeter is:
[tex]\begin{gathered} \text{Perimeter = }\frac{9\text{ }}{4}t-5+4t+3+\frac{1}{2}t-1+3t+2 \\ =\frac{39}{4}t-1 \end{gathered}[/tex]