The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. What are the dimensions of the garden?PLEASE HELP I KEEP TRYING TO DO IT BUT IT DOESN'T WORK.
Accepted Solution
A:
Answer:The dimensions of the garden areLength [tex]25.5\ ft[/tex] and Width [tex]16.5\ ft[/tex] Step-by-step explanation:Letx----> the length of the rectangular gardeny ---> the width of the rectangular gardenAw ----> the area of the walkwaywe know that[tex]x=y+9[/tex] ----> equation A[tex]Aw=(x+8)(y+8)-xy[/tex][tex]Aw=400\ ft^{2}[/tex]so[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex][tex]400=8x+8y+64[/tex] ----> equation BSubstitute equation A in equation B[tex]400=8(y+9)+8y+64[/tex] [tex]400=8y+72+8y+64[/tex] [tex]400=16y+136[/tex] [tex]16y=400-136[/tex] [tex]y=16.5\ ft[/tex] Find the value of x[tex]x=16.5+9=25.5\ ft[/tex] thereforeThe dimensions of the garden areLength [tex]25.5\ ft[/tex] Width [tex]16.5\ ft[/tex]