The perimeter of parallelogram ABCD is 46 inches. What is DA?


3 in, 4 in, 8 in, 19 in

Solution:

Perimeter of parallelogram ABCD = 46 inches

Consider x as the length of DA

We know that in a parallelogram, the length of opposite sides are equal

AB and DC are the opposite sides

AB = DC

8x - 5 = 3x + 10

By further calculation

8x - 3x = 10 + 5

5x = 15

x = 3

As the value of x is 3

Length of AB = 8x - 5 = 8 (3) - 5 = 24 - 5 = 19

AD and BC are equal as they are opposite sides

So the Perimeter = AB + BC + CD + DA

Substituting the values

46 = 2(AB) + 2(DA)

46 = 2(19) + 2(DA)

So we get,

46 = 38 + 2DA

2DA = 46 - 38

2DA = 8

Divide both sides by 2

DA = 4

Therefore, the value of DA is 4.

The perimeter of parallelogram ABCD is 46 inches. What is DA?

Summary:

The value of DA is 4 if the perimeter of parallelogram ABCD is 46 inches.

Math worksheets and
visual curriculum