Question

39) Ben builds a fence around a
rectangular garden. The perimeter of
the garden is 64 ft. The width is 12 ft
less than the length. Find the width
of the garden.

Answer 1

The width of the garden is 10 feet, if the perimeter of the garden is 64 feet and the width of the garden is 12 feet less than the length.  

Step-by-step explanation:

The given is,

              Shape of garden is rectangular

              Perimeter of garden - 64 feet

              Width of the garden is 12 feet less than the length.

Step: 1

             Formula to calculate the perimeter of the rectangle,

                               $P = 2(l+w)$........................(1)

            Where, l - Length of rectangle

                       w - Width of rectangle

Step: 2

           From the given data,

           Let, x = Length of the garden

                      P = 64 feet

                      w = x - 12 feet

          Equation (1) becomes,

                        64 = 2 ( x + (x - 12) )

                         $\frac{64}{2}$ = ( x + x - 12 )

                        32 = ( 2x - 12 )

                32 + 12 = 2x

                       44 = 2x

                         $x = \frac{44}{2}$

                    l = x = 22 feet

           width, w = x - 12 = 22 - 12

                     w = 10 feet

Step: 3

          Check for solution,

                       64 = 2 ( 12 + 22 )

                            = 2 (32)

                      64 = 64

Result:

        The width of the garden is 10 feet, if the perimeter of the garden is 64 feet and the width of the garden is 12 feet less than the length.