Question

The screen aspect of a widescreen tv is 16.9. What are the width and height of a 32 inch tv? Round answer to the nearest tenth of an inch.

Answer 1

check the picture below.

thus



`\bf 32^2=w^2+\left( \cfrac{9w}{16} \right)^2\implies 32^2=w^2+\cfrac{(9w)^2}{16^2}\implies 32^2=w^2+\cfrac{9^2w^2}{16^2} \\\\\\ 32^2=\cfrac{16^2w^2+81w^2}{16^2}\implies 32^2\cdot 16^2=337w^2 \\\\\\ (32\cdot 16)^2=337w^2\implies √((32\cdot 16)^2)=√(337w^2) \\\\\\ 32\cdot 16=w√(337)\implies \cfrac{32\cdot 16}{√(337)}=w\implies \boxed{\cfrac{512}{√(337)}=w}\\\\ -------------------------------\\\\`

and we can rationalize that to
`\bf \cfrac{512}{√(337)}\cdot \cfrac{√(337)}{√(337)}\implies \boxed{\cfrac{512√(337)}{337}}`

thus, its height is
`\bf h=\cfrac{9w}{16}\implies h=\cfrac{9}{16}\cdot \cfrac{512√(337)}{337}\implies \boxed{h=\cfrac{4608√(337)}{5392}}`