Widescreen monitor

A wave of widescreen monitors and televisions hit computer businesses. Calculate the area of ​​the LCD monitor with a diagonal size 27 inches at a ratio of 4:3 and then a 16:9 aspect ratio.

Is buying widescreen monitors with the same diagonal more advantageous than buying a 4:3 monitor?

Correct answer:

S₁ =  2257.5439 cm²
S₂ =  2009.683 cm²

Step-by-step explanation:

$$\begin{gathered} 1inc{h}^2=(2.54cm{)}^2=6.4516c{m}^2 \\ {k}_1=2.54^2=6.4516 \\ u=27\text{inch} \\ {r}_1=\frac{4}{3}\doteq 1.3333 \\ {r}_2=\frac{16}{9}\doteq 1.7778 \\ {z}_1=\sqrt{r_1^2+1}=\sqrt{1.3333^2+1}=\frac{5}{3}\doteq 1.6667 \\ {z}_2=\sqrt{r_2^2+1}=\sqrt{1.7778^2+1}\doteq 2.0397 \\ {b}_1=\frac{u}{z_1}=\frac{27}{1.6667}=\frac{81}{5}=16.2\text{in} \\ {a}_1=r_1\cdot b_1=1.3333\cdot 16.2=\frac{108}{5}=21.6\text{in} \\ {S}_1=a_1\cdot b_1\cdot k_1=21.6\cdot 16.2\cdot 6.4516=2257.5439{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} b_2=\frac{u}{z_2}=\frac{27}{2.0397}\doteq 13.2371\text{in} \\ {a}_2=r_2\cdot b_2=1.7778\cdot 13.2371\doteq 23.5325\text{in} \\ {S}_2=a_2\cdot b_2\cdot k_1=23.5325\cdot 13.2371\cdot 6.4516\doteq 2009.683{\text{cm}}^2 \\ {S}_2<S_1 \end{gathered}$$

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