Can someone help me solve this story problem?
Tom is buying a 42 inch 1080 television on sale for 40% off. If the aspect ratio is 16:9 and the frame around the screen is 1 inch wide,will it fit in an entertainment center with an opening that is 36 inches by 24 inches? Show work that supports the conclusions (remember that televisions are measured diagonally).
diagonal in opening: sqrt(36^2+24^2)
12*sqrt(9+4)=46.47inches
Now diagonal of TV
Now W=9/16 L
we need width and Length.
42^2=w^2 + L^2
42^2=(9/16)^2 L^2 +L^2
L^2=42^2*(25/16)^2
L=42*5/4=52inches Too big.