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. A 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

Explanation:

For any parallelogram, the opposite sides are the same length. Think of a rectangle, though we could have angles that aren't 90 degrees.

(5n-6) and (3n-2) are the lengths of the opposite sides. Set them equal to one another and solve for n.

5n-6 = 3n-2

5n-3n = -2+6

2n = 4

n = 4/2

n = 2

We can use this to find the length of the opposite sides

5n-6 = 5*2-6 = 10-6 = 4

3n-2 = 3*2-2 = 6-2 = 4

We get 4 each time which helps confirm we have the correct value for n.

The opposite sides are 4 cm each. The other side is

2n+3 = 2*2+3 = 4+3 = 7

Looking at adjacent sides (sides that are next door neighbors), we see 4 cm and 7 cm.

We could easily say "7 cm and 4 cm" as order doesn't matter. Though this isn't listed so we'll go with "4 cm and 7 cm" instead.

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y