Question

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 cm

Answer 1

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 $(5n-6)cm$ and $(3n-2)cm$ have the same lenght, then:

$5n-6=3n-2$

Now you have to solve for "n":

Add 6 to both sides of the equation.

Subtract 3n to both sides of the equation:

$5n-6+(6)-(3n)=3n-2+(6)-(3n)\\5n-3n=-2+6\\2n=4$

Divide both sides of the equation by 2:

$\frac{2n}{2}=\frac{4}{2}\\\\n=2$

To know the lenght of two adjacent sides, susbtitute $n=2$ into the third side $(2n + 3)cm$ and into one of the the sides that are opposite to eache other. Then:

$(2(2)+3)cm=7cm\\\\(5(2)-6)cm=4cm$