In a parallelogram, opposite sides are equal. This means that AD=BC.
Since AD=3x+4 and BC=x+15, we have
[tex]3x+4=x+15[/tex]
If we move x to the left hand side as -x and 4 to the right hand side as -4, we obtain,
[tex]3x-x=15-4[/tex]
then, x is equal to
[tex]\begin{gathered} 2x=11 \\ x=\frac{11}{2} \end{gathered}[/tex]
Now, we must substitute this values into AD and BC. We have for AD,
[tex]\begin{gathered} AD=3x+4 \\ AD=3\cdot\frac{11}{2}+4 \\ AD=\frac{33}{2}+4 \\ AD=\frac{33}{2}+\frac{8}{2} \\ AD=\frac{33+8}{2} \\ AD=\frac{41}{2} \end{gathered}[/tex]
and for BC, we have
[tex]\begin{gathered} BC=x+15 \\ BC=\frac{11}{2}+15 \\ BC=\frac{11}{2}+\frac{30}{2} \\ BC=\frac{11+30}{2} \\ BC=\frac{41}{2} \end{gathered}[/tex]
which is an expected result because AD=BC. However, its a checking for our computations.
In summary, the answers are:
[tex]\begin{gathered} x=\frac{11}{2} \\ AD=BC=\frac{41}{2} \end{gathered}[/tex]
