let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

the length of a rectangle is 1cm less than four times its width

l = 4w - 1

the area of the rectangle is 39cm^2

l*w = 39

plug l = 4w - 1 into the last equation:

(4w - 1)*w = 39

by solving we find:

w = 3.25 cm

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

l = 4*3.25 - 1

l = 12 cm

the dimensions of the rectangle are: the length is 12 cm and the width is 3.25 cm.