let

x = the length, x>0

y = the width, y>0

the length of a rectangular garden exceeds the width by 10 ft:

y = 10 + y

the perimeter is 48 ft:

2(x + y) = 48 divide both sides by 2

x + y = 24

by solving the system of equations:

x = 10 + y

x + y = 24

we find:

x = 17 ft

y = 7 ft

click here to see the step by step solution of the system of equations:

the dimensions of the rectangle are 17 ft and 7 ft.