# A screen

A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?

Correct result:

a =  965
b =  603
x0 =  358
y0 =  224
x1 =  2038
y1 =  224
x2 =  2038
y2 =  1274
x3 =  358
y3 =  1274

#### Solution:

$w=1680 \ \\ h=1050 \ \\ \ \\ p=33 \%=\dfrac{ 33 }{ 100 }=0.33 \ \\ \ \\ a=w \cdot \ \sqrt{ p }=1680 \cdot \ \sqrt{ 0.33 }=168 \ \sqrt{ 33 }=965$
$b=h \cdot \ \sqrt{ p }=1050 \cdot \ \sqrt{ 0.33 }=105 \ \sqrt{ 33 }=603$
$x_{0}=w/2-a/2=1680/2-965.0865/2=\dfrac{ 715 }{ 2 }=358$
$y_{0}=h/2-b/2=1050/2-603.1791/2=\dfrac{ 447 }{ 2 }=224$
$x_{1}=x_{0}+w=357.5+1680=2038$
$y_{1}=y_{0}=223.5=224$
$x_{2}=x_{0}+w=357.5+1680=2038$
$y_{2}=y_{0}+h=223.5+1050=1274$
$x_{3}=x_{0}=357.5=358$
$y_{3}=y_{2}=1274$

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