Since you keep proportional dimensions, the proportion between the old and new dimensions must be the same. So, if we call the new height [tex] h [/tex], the preservation of the width/height ratio is written as
[tex] 4 \div 6 = 9 \div h [/tex]
Solving the proportion for [tex] h [/tex] yields
[tex] h = \frac{6\cdot 9}{4} =\frac{3\cdot 9}{2} = \frac{27}{2} = 13.5 [/tex]
