Given:
The perimeter of the pentagon, P=56 units.
From the figure, the sides of the pentagon are 2x, 10, x+2, 3x-2 and 10.
The sum of sides of the pentagon is equal to its perimeter.
Hence, the perimeter can be expressed as,
[tex]\begin{gathered} P=2x+x+2+3x-2+10+10 \\ P=6x+20 \end{gathered}[/tex]
Now, put P=56 in the above equation and solve for x.
[tex]\begin{gathered} 56=6x+20 \\ 56-20=6x \\ 36=6x \\ \frac{36}{6}=x \\ 6=x \end{gathered}[/tex]
Therefore, the value of x is 6.
