let 'x' and 'y' be the length of the sides of a rectangular window, x>0, y>0

the length of the sides of a rectangular window have the ratio 1.5 to 1

x : y = 1.5 : 1

x/y = 1.5/1

x/y = 1.5 multiply both sides by y

x = 1.5y

the area of the window is 1,350 square inches

x*y = 1350

plug x = 1.5y into previous equation

(1.5y)y = 1350

by solving the quadratic equation we find and consider the positive roots

y = 30 in

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x = 1.5*y = 1.5*30 = 45 in

the dimensions of the window are 30 inches and 45 inches.