Question

Find the width and height of a 100in television that has an aspect ratio of 4:3.

A. width- 20in
height- 60in

B. width- 60in
height- 80in

C. width- 80in
height- 60

D. width- 60in
height- 20in

Answer 1

let's bear in mind that TV sets are sold as having so many inches, that refers to their diagonal distance, check the picture below.

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{100}\\ a=\stackrel{adjacent}{4x}\\ b=\stackrel{opposite}{3x}\\ \end{cases}\implies 100^2=(4x)^2+(3x)^2 \\\\\\ 10000=(4^2x^2)+(3^2x^2)\implies 10000=16x^2+9x^2\implies 10000=25x^2 \\\\\\ \cfrac{10000}{25}=x^2\implies 400=x^2\implies √(400)=x\implies 20=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{w=4x}{80}\qquad \stackrel{h=3x}{60}~\hfill`