Question

in parallelogram ABCD, AB=(6x-2) feet DC=(3x+13) feet and AD=5 feet. Find the number of feet in the perimeter of the parallelogram

Answer 1

66 feet

Explanation:

Parallelograms have 2 pair of parallel sides that are congruent to each other.

In parallelogram ABCD, we can say:

AB = DC

and

BC = AD

AB and DC are given, and they are equal. So we can say:

AB = DC

6x - 2 = 3x + 13

Now we can solve for x:

6x - 2 = 3x + 13

6x - 3x = 13 + 2

3x = 15

x = 15/3

x = 5

So,

AB = 6x - 2

AB = 6(5) - 2 = 28

So, DC = 28

We are also given AD = 5, so BC = 5 as well [since AD = BC]

Now, we know the length of all 4 sides.

The perimeter is the sum of all 4 sides. Hence,

Perimeter = 28 + 28 + 5 + 5 = 66 feet