# Math Help - measurents of TV

1. ## measurents of TV

A STANDARD picture format TV has a screen where the width is 4/3 of the height.
A WIDESCREEN TV has a screen where the width is 16/9 of the height.
Consider 2 TVs that are the same size, which means that the diagonals(28 inches= 2.54cm) of the screens are the same length, but where one of them is of the standard pic format and the other one- widescreen.

Determine screen wil have the largest area.

2. considering th standard one first:

given that the width is 4/3 of the height

height, h = h
width, w = $\frac{4}{3}h$

also given that that size of the TV is 28 inches(71.12 cm), this is actually the hypotenuse of the TV

$
28^2 = h^2 + w^2
$

$
28^2 = h^2 + {(\frac{4}{3}h)}^2
$

$
784 = h^2 + \frac{16}{9}h^2
$

$
784 = \frac{25}{9}h^2
$

$
h^2 = 282.24 inches
$

$
h = 16.8 inches
$

Area of the screen
= area of a rectangle with a diagonal of 28 inches
$
=width \times height
$

$
=\frac{4}{3}h\cdot h
$

$
=\frac{4}{3} h^2
$

$
= \frac{4}{3} (282.24)
$

$
= 376.32 inches^2
$

do the same thing for the widescreen TV and i get 335.003 inches^2. Hence concluding that the standard picture TV has a larger area.

3. Thank u!