Question

Find the area of a 36-inch TV,with aspect ratio of 4:3 ( round to the nearest hundredth)

Answer 1

let

a = height of Tv

b = width

c = diagonal

The diagonal of the Tv is 36 inches. Therefore we can use pythagoras theorem to find side a and b in other to get the area of the Tv.

`\begin{gathered} a^2+b^2=c^2 \\ (b)/(a)=(4)/(3) \\ 4a=3b \\ a=(3b)/(4) \\ ((3b)/(4))^2+b^2=36^2 \\ square\text{ root both sides} \\ (3b)/(4)+b=36 \\ (3b+4b)/(4)=36 \\ (7b)/(4)=36 \\ 7b=144 \\ b=(144)/(7) \\ b=20.5714285714 \\ a^2+b^2=c^2 \\ c^2-b^2=a^2 \\ 36^2-20.5714285714^2=a^2 \\ 1296-423.1249=a^2 \\ 872.876=a^2 \\ a=√(872.876) \\ a=29.5444749488 \end{gathered}`
`\begin{gathered} \text{area}=\text{ }29.5444749488*20.57=607.729849697 \\ \text{area }\approx607.73unit^2 \end{gathered}`