TV diagonal

Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?

Result

a =  48.808 cm
b =  27.455 cm

Solution:

d=0.56 m=0.56 100 cm=56 cm a:b=16:9 d2=a2+b2  d2=a2+(9/16 a)2 d2=a2+(9/16)2 a2  a2=d21+(9/16)2  a=d1+(9/16)2  a=d 16/162+92=56 16/162+9248.808248.808 cmd=0.56 \ m=0.56 \cdot \ 100 \ cm=56 \ cm \ \\ a:b=16:9 \ \\ d^2=a^2 + b^2 \ \\ \ \\ d^2=a^2 + (9/16 \cdot \ a)^2 \ \\ d^2=a^2 + (9/16)^2 \cdot \ a^2 \ \\ \ \\ a^2=\dfrac{ d^2 }{ 1 + (9/16)^2 } \ \\ \ \\ a=\dfrac{ d }{ \sqrt{ 1 + (9/16)^2 } } \ \\ \ \\ a=d \cdot \ 16/\sqrt{ 16^{ 2 }+9^{ 2 } }=56 \cdot \ 16/\sqrt{ 16^{ 2 }+9^{ 2 } } \doteq 48.8082 \doteq 48.808 \ \text{cm}
b=916 a=916 48.8082=27.4545=27.455 cmb=\dfrac{ 9 }{ 16 } \cdot \ a=\dfrac{ 9 }{ 16 } \cdot \ 48.8082=27.4545=27.455 \ \text{cm}



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#
Lilymay
why did it have to be divided by the square root of 16 and 9 squared?

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