Dimensions of a rectangle

Question

The length of a rectangle is one foot more than three times its width. If the perimeter is 98 feet, what are the dimensions of the rectangle?

Answer 1

Hi Kayla! 

 

The first thing we should do is set up some variables:

Let L= the length of the rectangle in feet (ft)

Let w= the width of the rectangle in ft

Let p= the perimeter of the rectangle in ft

 

The given problem tells us the following:

p= 98

L= 1 + 3w

 

We also know that perimeter is the sum of all the rectangle's sides, which we can write as:

p=2L + 2w (since the rectangle has two long sides and two short sides!)

 

Now, we're going to want to substitute some things:

98= 2L + 2w

 

Since we still have two unknown variables, we need to substitute again:

98=2(1+ 3w) + 2w  <-- now we can solve this!

98= 2 + 6w + 2w

98= 2 + 8w

96= 8w

w= 12

 

Now that we know the width, we can figure out the length:

L= 1 + 3w

L= 1 + 3(12)

L= 1 + 36

L= 37

 

The width of the rectangle is 12 feet, and the length is 37 feet. 

 

Hope this clears things up! -Rachel

 

Answer 2

perimeter = 98 = 2L + 2W; divide all terms by two to simplify, getting 49 = L + W ⇐*

L = 1 + 3W <---see first sentence

 

substitute for L in the starred equation above (*):  49 = (1 + 3W) + W

49 = 1 + 4W

48 = 4W

12 = W

 

so L = 1 +3•12 = 37.   The dimensions are 12' by 37'.  Note the use of ' meaning ft, just as " means inches.