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. 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:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So, set up the equation $5n−6 = 3n−2$.
$5n−3n=-2 + 6$
$2n=4$
$n = 2$.

Step2: Find the lengths of the sides

First, find the length of the side with expression $5n−6$ or $3n−2$. Substitute $n = 2$ into $5n−6$: $5\times2−6=10 - 6=4$ cm.
Then, find the length of the third - side with expression $2n + 3$. Substitute $n = 2$ into $2n+3$: $2\times2+3=4 + 3=7$ cm.

Answer:

B. 4 cm and 7 cm