Q:

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram? 2 cm and 2 cm 4 cm and 7 cm 7 cm and 9 cm 13 cm and 19 cmJuanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram? 2 cm and 2 cm 4 cm and 7 cm 7 cm and 9 cm 13 cm and 19 cm

Accepted Solution

A:
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]