let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

the length of a rectangle is 3cm shorter than twice the width

l = 2w - 3

the area of the rectangle is 20cm

l*w = 20

plug l = 2w - 3 in the above equation

(2w - 3)w = 20

by solving the quadratic equation

(2w - 3)w = 20

we find and consider the positive roots only since w>0

w = 4 cm

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l = 2w - 3 = 2*4 - 3 = 5 cm

the dimensions of the rectangle are 5 cm and 4 cm.