Question

Can someone help with this math problem

Answer 1

Answer:

20 ft long; 12 ft wide

Step-by-step explanation:

Let   w = the width of the garden

Then l = w + 8

       A = lw

       A = (w + 8)w

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The sidewalk is 4 ft wide, so, for the big rectangle consisting of garden plus sidewalk:

Width   = w +8

Length = w + 16

   Area = (w + 8)(w + 16)

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The difference between the two areas is the area of the sidewalk (320 ft²).

(w + 8)(w + 16) - (w + 8)w = 320     Factor out w + 8

         (w+ 8)(w + 16 – w) = 320      Combine like terms

                     (w+ 8) × 16 = 320      Divide each side by 16

                             w + 8 = 20        Subtract 8 from each side

                                   w = 12 ft

                                    l = 12 + 8

                                   l = 20 ft

The garden is 20 ft long by 12 ft wide.