The area of a trapezoid is given by:
[tex]A=\frac{1}{2}\cdot h\cdot(a+b).[/tex]Where:
• h is the heigh,
,• a and b are the length of the parallel sides.
In this problem, we have:
• A = 180 cm²,
,• h = 18 cm,
• a = 5 cm,
,• b = x.
Replacing these data in the equation above, we have:
[tex]180cm^2=\frac{1}{2}\cdot18\operatorname{cm}\cdot(5\operatorname{cm}+x)\text{.}[/tex]Solving for x the last equation, we get:
[tex]\begin{gathered} \frac{2\cdot180cm^2}{18\operatorname{cm}}=5\operatorname{cm}+x, \\ 20\operatorname{cm}=5\operatorname{cm}+x, \\ x=20\operatorname{cm}-5\operatorname{cm}, \\ x=15\operatorname{cm}\text{.} \end{gathered}[/tex]So the length of the second parallel side is:
[tex]x=15\operatorname{cm}\text{.}[/tex]Answer: 15 cm
