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

Second option: 4 cm and 7 cm.

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:

`(2n)/(2)=(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`