Word Problem

Question

The length of a dog kennel is 4 feet longer than its width. If the perimeter is 52 feet, what is the length and width. Please show all work.

Answer 1

The key to word problems is to translate the words and phrases into concise, precise math expressions (variables and operations).

 

If possible, assign variables to the values the problem asks you to find.  In this problem:

    "What is the length and width"     means

                        L = length

                         W = Width

                     Report L.W

Translate:

    "The length .. is 4 feet longer than the width"    mans    L = 4 + W

    "The perimeter is 52 ft," means   P=52=L+W+L+W      {Perimeter is distance around; we assume rectangle)

 

Now, the easy math.  Either substitute or eliminate -- let's use L=4+W to substitute for L.

        52 = (4+W) + W + (4+W) + W

        52 = 8 + 4W          (collect terms)

        44 = 4W                 (subtract 16 from both sides)

         11 = W

 

Putting the value of W in either equation (now, which is easier?):

         L = 4 + W

         L = 4 + 11

         L = 15

 

Checking (very important):

  Is  P=52= 15 + 11 + 15 + 11      ?

            52 = 52     ?  Yes !