A rectangular yard has area 96 square feet. If the width of the yard is 4 feet less than the length, what is the perimeter, in feet, of the yard?

Question

I'm given the exact area of a rectangle and its width in terms of how many feet it is less than the length. I have to find the perimeter of the rectangle.

Answer 1

Victor the perimeter is 40 feet.

 

Victor you know to find the area of a rectangle you multiply the length by the width.

Area = 96 square feet.  ( Clue: Think about the factors of 96.

12 x 8 = 96. 

Therefore Length = 12 feet, Width = 8 feet (  Width = L   - 4 feet)  

                                                                  Width = 12 feet - 4 feet = 8 Feet

                                               Therefore the Width  is 8 feet

Perimeter=      L    +  L       + W +    W

                 12 feet  + 12 feet +8 feet  + 8 feet = 40 feet

 

Perimeter = 40 feet

Answer 2

In order to find the perimeter, you need to know the width and the length (not just how they relate to each other).

     P = 2(l+w)

 

And, in order to find the length and width, we can use their relationship along with the area of the yard (96 ft^2).

      A =l*w = 96

            l = 96/w      (divide both sides by w)

 

       w = l - 4                (width is 4 feet less than length)

       w  =  (96/w) - 4          (substitute value for l)

       w^2 = 96 - 4w           (multiply everything by w)

       w^2 + 4w -96 = 0         (put everything on one side)

                                      (now, either factor or use quadratic formula)

       (w-8)(w+12) = 0      (roots are 8 and -12, bit -12 doesn't make sense for a dimension)

         w = 8

         l = 96/w = 96/8

         l = 12

 

Check:  Is  A=96 = 8*12 ?   yes.