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 . The horizontal length of a “-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]