the length of a rectangular garden is 8 feet longer than its width. the garden is surrounded by a sidewalk that is 4 feet wide and has an area of 320 square feet. find the dimensions of the garden
width --- x
length -- x+8
area of garden without sidewalk = x(x+8) = x^2 + 8x
including the sidewalk:
width = x+8
length = x+8+8 = x + 16
area of whole garden = (x+8)(x+16) = x^2 + 24x + 128
x^2 + 24x + 128 - x^2 - 8x = 320
16x = 192
x = 12
the garden without the side-walk is 12 ft by 20 ft
including the sidewalk the garden is 20 by 28
note (20)(28) - (12)(20) = 560 - 240 = 320