MathDB
Big TV Screen

Source:

January 4, 2009
geometryrectangleratio

Problem Statement

Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3 4 : 3. The horizontal length of a “27 27-inch” television screen is closest, in inches, to which of the following? [asy]import math; unitsize(7mm); defaultpen(linewidth(.8pt)+fontsize(8pt));
draw((0,0)--(4,0)--(4,3)--(0,3)--(0,0)--(4,3)); fill((0,0)--(4,0)--(4,3)--cycle,mediumgray); label(rotate(aTan(3.0/4.0))*"Diagonal",(2,1.5),NW); label(rotate(90)*"Height",(4,1.5),E); label("Length",(2,0),S);[/asy]<spanclass=latexbold>(A)</span> 20<spanclass=latexbold>(B)</span> 20.5<spanclass=latexbold>(C)</span> 21<spanclass=latexbold>(D)</span> 21.5<spanclass=latexbold>(E)</span> 22 <span class='latex-bold'>(A)</span>\ 20 \qquad <span class='latex-bold'>(B)</span>\ 20.5 \qquad <span class='latex-bold'>(C)</span>\ 21 \qquad <span class='latex-bold'>(D)</span>\ 21.5 \qquad <span class='latex-bold'>(E)</span>\ 22