The path around a square flower bed is 3 feet wide. If the area of the flower bed is equal to the area of the path, find the dimensions of the flower bed.

Answer 1

area of bed = x^2

area of whole figure = (x+6)^2

area of path = (x+6)^2 - x^2
so
x^2 + 12 x + 36 -x^2 = x^2

-x^2 + 12 x + 36 = 0
x^2 - 12 x - 36 = 0
(x-6)(x-6) = 0
x = 6