If Width = 4/3 Height, then you can substitute into the Pythagorean theorem and solve.

Pythagoras tells us the length of the Diagonal

27

729 = Height

729 = (1 + 16/9) (Height)

729/(1+ 16/9) = Height

Height = √(729/(1+16/9))

Height = 16.2

Width = 4/3 (16.2)

Width = 21.6

Now let's check it;

16.2

16.2

√729 = 27

So it checks. You could also solve this using trig relationships.

Pythagoras tells us the length of the Diagonal

^{2}is equal to the Height^{2}x Width^{2}27

^{2}= Height^{2}x (4/3 Height)^{2}729 = Height

^{2}x (4/3)^{2}(Height)^{2}729 = (1 + 16/9) (Height)

^{2}729/(1+ 16/9) = Height

^{2}Height = √(729/(1+16/9))

Height = 16.2

Width = 4/3 (16.2)

Width = 21.6

Now let's check it;

16.2

^{2}+ 21.6^{2}= ?16.2

^{2}+ 21.6^{2}= 729√729 = 27

So it checks. You could also solve this using trig relationships.