A land mass is roughly in the shape of a rectangle whose perimeter is 1220 miles. The width is 110 miles less than the length. What is the width?

Question

A land mass is roughly in the shape of a rectangle whose perimeter is 1220 miles. The width is 110 miles less than the length. What is the width?

Answer 1

Let:

  L = length of land mass

  W = width of land mass

 

Translate:

  "rectangle ... perimeter is 1220 miles"     means   P = 1220 = 2L + 2W       [eq1]

  "width is 110 miles less than the length"    means    W =  -110 + L              [eq2]

  "What is the width?"     means      report W

 

The math:

     2L   +  2W   =  1220                 [re-written eq1]

     2L   +  2(L-110)  = 1220           [substitute for W using eq2]

     2L + 2L - 220 = 1220               [distribute 2]

          4L - 220 = 1220                 [collect terms]

             4L  =  1440                    [subtract 220 from both sides]

              L   =  360

 

Put value of L into either equation to solve for W  [let's use eq2]:

             W = -110 + 360

             W = 250

 

Now, check (very important):

  Is  2(250) + 2(360) = 1220   ?

        500 + 720  =  1220   ?

             1220  =  1220   ?yes

  Is     250  =  -110 + 360   ?

            250 = 250   ?yes

 

(note:  If this problem appears on a test and you are rushing, you might substitute for L (L=W+110 from eq2) into eq1 to eliminate L.  This gives a quick result for W.  However, you should always, always consider the effect of typos (even using a calculator), or simple errors in copying equations, etc.  Math problems usually demand a level of accuracy!

Answer 2

Hi Nyala, 

Step One: Givens

Perimeter is 1220

Width is length-110

Length is length

Step Two: Equation

Perimeter=length+length+width+width

1220=length+length+(length-110)+(length-110) Distribute the 1

1220=2length+length-110+length-110 Combine like terms

1220=4length-220 Add 220 to both sides

1440=4length Divide both sides by 4

360=length

∴Length is 360 miles and width is 250 miles.

Best, 

Starlyte H.