Answer:
Second option: 4 cm and 7 cm.
Step-by-step explanation:
A Parallelogram is defined as a type of Quadrilateral, whose opposite sides are parallel and have equal lenght.
Since the opposite sides [tex](5n-6)cm[/tex] and [tex](3n-2)cm[/tex] have the same lenght, then:
[tex]5n-6=3n-2[/tex]
Now you have to solve for "n":
Add 6 to both sides of the equation.
Subtract 3n to both sides of the equation:
[tex]5n-6+(6)-(3n)=3n-2+(6)-(3n)\\5n-3n=-2+6\\2n=4[/tex]
Divide both sides of the equation by 2:
[tex]\frac{2n}{2}=\frac{4}{2}\\\\n=2[/tex]
To know the lenght of two adjacent sides, susbtitute [tex]n=2[/tex] into the third side [tex](2n + 3)cm[/tex] and into one of the the sides that are opposite to eache other. Then:
[tex](2(2)+3)cm=7cm\\\\(5(2)-6)cm=4cm[/tex]
