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The perimeter of a rectangular picture is 66 in. The length is 3 in. greater than the width. Find the width and length.

need to know the width and length

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Okay, well we start out with the equation P=66, where P is perimeter. You should create equations using variables to explain each piece of information you are given. Follow the equations below and see if you can understand how to do another one like this. In this problem, l is length and w is width.

P = 66                               The perimeter is equal to 66

l = 3 + w                           The length of one side is 3 more than the width

2l + 2w = 66                      A rectangle's perimeter is calculated by adding the lengths and widths

2(3 + w) + 2w = 66           Use what you know about length from step 2 to replace the variable in step 3

6 + 2w + 2w = 66              Multiply

6 + 4w = 66                       Add like terms

4w = 60                            Subtract

w = 15                             Divide

l = 3 + w                         Remember step 2?

l = 3 + 15                       Replace the variable using your value for w

l = 18                             Add

And you're done! Always check your work. It helps to create a picture of a rectangle while you're doing these problems as well. As you get used to these problems more and more, you can show more or less work than I've shown, but try to stay true to what the teacher asks of you. Good luck!


Great explaination.  As you said drawing a picture is always a good first step.

The perimeter of a rectangular picture is 66 in. The length is 3 in. greater than the width. Find the width and length.

I use an Acronym to handle many word problems like this.  The Acronym is M.A.P.E.X.

The length is 3 in greater than the width      M. ost unknown = x

So let x = width

                                                                A. ssign variables

So if x = width then length is ?      Length = x +3

                                                               P. icture  (draw picture for this setup)

      x+3 = length

|                                                       |     x = width

|_______________________________ |

                                                           E. quation that fits the picture and other numbers not used yet

Well the number 66 was not used yet and it represents the perimeter.   Well you can either remember that the perimeter is the equation  P = 2L +2W    so   P = 2(x+3) + 2(x)    or understand the nature of finding any perimeter is to sum all the sides of this object.

So  (x+ 3)  + x  + (x +3) +x  = 66     (notice opposite sides are the same length and that we are not done until we have added four of the sides.

Either way it gives the equation

4x + 6 = 66      Subtract 6

4x + 6 - 6  = 66- 6

4x  = 60     now divide by coefficient on x

4x/4  = 60/4

x = 15                                     eX. amine your answer 

Well we solved for x but what does x represent .  From our original setup x = width  so our width is 15 inches or whatever units.  And did solving for x answer the question.

If the question was find the dimensions or find the length we have to go back in and solve for the length by plugging our answer x= 15 into our expression x + 3

Length = x +3  = 15 +3  = 18 inches

A final check would be to determine if these values do in fact add to a perimeter that is 66

2(18)  + 2(15) = 66

36 + 30 = 66

66= 66



Perimeter of a rectanlgle = 2(L+W) = 66 (given)

But the Length is 3 ft more than width →  L = W + 3

Therefore 2(W+3+W) = 66

2(2W+3) = 66

Divide by 2 on boths sides


subtract 3 from both sides



divide by 2 on both sides

W = 15

L= W+3 = 15+3= 18