If the length of the rectangular parking lot is 10 meters less than twice its width, and the perimeter is 400 meters, find the length of the parking lot

Question

This story problems has to be solved using algebraic equation  

Answer 1

First, read the problem until you understand it.  Drawing a picture often helps.

 

Then, assign variables.  If possible, assign a variable to the value the problem asks you to find.  Here it is "length," so

  let L=length

      W = width

 

Translate:

 "rectangular ... perimeter is 400 meters"     means   P = L+W+L+W = 2L + 2W = 400m

                      2L + 2W = 400

         

 "length ... is 10 meters less than twice its width"         means

       L        =       -10           +          2W

 

Now, the easy math:

  Let's use the elimination method --

      2L + 2W = 400

        L -  2W = -10         (second equation rewritten)

   ---------------------

       3L         = 390          (add equations)

         L  = 130                 (divide both sides by 3)

 

Now, put that into either equation  to solve for W:

       130 = -10 + 2W

        140 = 2W               (add 10 to both sides)

           70 = W                (divide both sides by 2)

 

Checking (very important):

  Is  2(130) + 2(70) = 400    ?

       260  + 140   = 400     ?

           400 = 400    ? yes

   

     

Answer 2

L=length, W=width

L=2W-10 the condition given

L+L+W+W=400 the perimeter

2L+2W=400

L+W=200

2W-10+W=200

3W=210

W=70

L=130