If Width = 4/3 Height, then you can substitute into the Pythagorean theorem and solve.
Pythagoras tells us the length of the Diagonal2 is equal to the Height2 x Width2
272 = Height2 x (4/3 Height)2
729 = Height2 x (4/3)2 (Height)2
729 = (1 + 16/9) (Height)2
729/(1+ 16/9) = Height2
Height = √(729/(1+16/9))
Height = 16.2
Width = 4/3 (16.2)
Width = 21.6
Now let's check it;
16.22 + 21.62 = ?
16.22 + 21.62 = 729
√729 = 27
So it checks. You could also solve this using trig relationships.
Pythagoras tells us the length of the Diagonal2 is equal to the Height2 x Width2
272 = Height2 x (4/3 Height)2
729 = Height2 x (4/3)2 (Height)2
729 = (1 + 16/9) (Height)2
729/(1+ 16/9) = Height2
Height = √(729/(1+16/9))
Height = 16.2
Width = 4/3 (16.2)
Width = 21.6
Now let's check it;
16.22 + 21.62 = ?
16.22 + 21.62 = 729
√729 = 27
So it checks. You could also solve this using trig relationships.