let

x = the width in ft, x >= 0

y = the length in ft, y>=0

A rectangular garden is 2 ft longer than it is wide:

y = x + 2

Its area is 624 ft^2:

x*y = 624 (the area of rectangle = width*length)

plug y = x+1 into the last equation:

x*(x + 2) = 624

by solving we find:

x = 24 ft

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y = 24 + 2

y = 26 ft

width is 24 ft.

length is 26 ft.