let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

the length of the rectangle is 1 ft more than twice the width

l = 1 + 2w

the area of a rectangle is 45 ft square

A = l*w

l*w = 45

plug l = 1 + 2w into the last equation

(1 + 2w)w = 45

by solving we find

w = 4.5 ft

click here to see the step by step solution of the equation

l = 1 + 2*4.5

l = 10 ft

the dimensions of the rectangle are: the length is 10 ft and the width is 4.5 ft.