let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

the length of a rectangle is 3 cm more than the width

l = w + 3

the area is A = 70 cm^2

A = l*w

l*w = 70

plug l = w + 3 into l*w = 70 we get

(w + 3)*w = 70

by solving we find

w = 7 cm

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l = 7 + 3

l = 10 cm

the dimensions of the rectangle are 10 cm and 7 cm.