Answer:
[tex]AD=15[/tex]
Explanation: We know that in any given parallelogram the opposite sides are equal, therefore for the given parallelogram we can say the following:
[tex]DC=AB[/tex]
From this we can form the following equation for the sides:
[tex]DC=AB\rightarrow3x+5=6x-10\rightarrow(1)[/tex]
Solving (1) for x gives:
[tex]\begin{gathered} 3x+5=6x-10\rightarrow3x+5+10=6x \\ \therefore\rightarrow \\ 3x+15=6x\rightarrow15=6x-3x=3x\rightarrow3x=15 \\ \therefore\rightarrow \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]
Therefore the value of the AD side is:
[tex]\begin{gathered} AD=4x-5=4(\frac{15}{3})-5=4\times5-5=20-5=15 \\ \therefore\rightarrow \\ AD=15 \end{gathered}[/tex]
