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 answer:

a =  965
b =  603
x₀ =  357
y₀ =  223
x₁ =  2037.4567
y₁ =  223
x₂ =  2037.4567
y₂ =  1273.4105
x₃ =  357
y₃ =  1273.4105

Step-by-step explanation:

$$\begin{gathered} w=1680 \\ h=1050 \\ p=33\mathrm{\%}={\displaystyle \frac{33}{100}}=0.33 \\ a=w\cdot \sqrt{p}=1680\cdot \sqrt{0.33}=168\sqrt{33}=965 \end{gathered}$$

$b=h\cdot \sqrt{p}=1050\cdot \sqrt{0.33}=105\sqrt{33}=603$

$x_0=w\mathrm{/}2-a\mathrm{/}2=1680\mathrm{/}2-965.0865\mathrm{/}2=357$

$y_0=h\mathrm{/}2-b\mathrm{/}2=1050\mathrm{/}2-603.1791\mathrm{/}2=223$

$x_1=x_0+w=357.4567+1680=2037.4567$

$y_1=y_0=223.4105=223$

$x_2=x_0+w=357.4567+1680=2037.4567$

$y_2=y_0+h=223.4105+1050=1273.4105$

$x_3=x_0=357.4567=357$

$y_3=y_2=1273.4105$

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