A rectangle has a length six inches less than twice its width. If the perimeter of the rectangle is 54 inches, find the dimensions.

Answer 1

Hi Jehanna B.,

Let L = the length of the rectangle.

Let W = the width of the rectangle.

Let P = the perimeter

The perimeter of the rectangle is equal to twice the length plus twice the width, P = 2L + 2W.

And the rectangles length (L) is (=) six less than twice its width (2W - 6), L = 2W - 6.

We are also given the perimeter, P = 54. We can set P equal to 54 and substitute L = 2W -6 into P = 2L + 2W, and solve for W, then solve for L.

P = 2L + 2W

54 = 2(2W - 6) + 2W, (substitute P = 54 and L = 2W - 6)

54 = 4W - 12 + 2W, (multiplied through)

66 = 6W, (added 12 to both sides and add 4W + 2W)

11 = W, (divide both sides by 6)

Now we need to find the length (L) by substituting W = 11 into our perimeter equation:

P = 2L + 2W

54 = 2L + 2(11), (substitute P = 54 and W = 11)

54 = 2L + 22, (multiplied)

32 = 2L, (subtract 22 from both sides)

16 = L, (divided both sides by 2)

I hope this helps, Joe.

Answer 2

Let w = width and l = length. The length in this case is actually 2w -6.

Perimeter formula: P = 2l + 2w

Let's plug in our l and get the width first.

54 = 2(2w - 6) + 2w (plug in known values)

54 = 4w - 12 + 2w (multiplying)

66 = 6w (isolate the variable)

11 = w (solving for width)

Now to find length using the top equation

l = 2w - 6 (length equation based on given info)

l = 2 x 11 - 6 (plug in knowns)

l = 22 - 6 (multiplying)

l = 16 (solving for length)

The fence is 16 inches by 11 inches.

Answer 3

My favorite kind of story problems! Let's see if I can help you out...

Let's put this information into numerical form. Let's say our width is "W" and length is "L":

W = width

L = length

We know our length is 6 less than twice our width. This means if we multiply our width by 2 and subtract 6, we get our length:

W = width

L = 2W - 6

Now the perimeter formula is:

2W + 2L = P

Now we can plug everything in and simplify:

2W + 2(2W - 6) = 54

2W + 4W - 12 = 54

6W = 66

W = 11

L = 2(11) - 2 = 22 - 6 = 16

So our length is 16 and our width is 11. I hope this explanation is thorough and answered all of your questions. If you have additional questions please don't hesitate to reach out! Learn on! :)