The perimeter of a parallelogram is 44 meters. The width of the parallelogram is 6 meters less than its length.find the length and the width of the parallelogram.

Answer 1

First, let's clarify a few things. A parallelogram does not have length & width in the classic sense (i.e. like a rectangle), as those terms indicate overall dimensions.

So, for this answer I will assume that we are talking about the lengths of the two pairs of equal and parallel sides of the parallelogram.

In that case the perimeter of the parallelogram is the same as a rectangle of the same side lengths:

2a + 2b

Using the given 44 meters as the perimeter we get:

44 = 2a + 2b

Using "a" for the width, "b" for the length, and the description of the relationship between the two we get:

a = b - 6

Now we substitute b - 6 for a in the first equation and solve:

44 = 2(b - 6) + 2b | distribute the parenthesis

44 = 2b - 12 + 2b | combine like terms

44 = 4b - 12 | +12

56 = 4b | /4

14 = b

Using a = b -6 we get a:

a = 14 - 6

a = 8

Verify:

44 = 2*8 + 2*14

44 = 16 + 28

44 = 44

Checks out!

Answer 2

Let x = length

x-6 = width

Perimeter is all 4 sides added together

P = l+l+w+w substitute into the equation known values and expressions

44 = x+x+(x-6)+(x-6) combine like terms

44=4x-12 Add 12 to both sides

44+12 = 4x-12+12 simplify

56 = 4x divide both sides by 4

56/4=4x/4

14=x

14-6 = 8

The width is 8, the length is 14.

Answer 3

p = 2(l + w)

w = l - 6

These used to confuse me, too. Because two things are equal, we can sub them out for each other.

p = 2(l + (l - 6))

p = 2(2l - 6)

p = 4l - 12

Now, plug in what we are given.

44 = 4l - 12

44 + 12 = 4l - 12 + 12

56 = 4l

56/4 = 4l/4

14 = l

The length is 14 meters.

w = l - 6

w = 14 - 6

w = 8

The width is 6 meters.

Hope this helps!