Question

A movie with an aspect ratio of 1.95:1 is shown as a letterboxed image on a 72-inch 16:9 television. Calculate the height of the image, the area of the image, the height of each black bar at the top and the bottom of the screen, and area of each black bar on the screen.


Calculate x using Pythagorean’s thm







Calculate width and height and area of TV (Area= width*height)




Which dimension is the same between the image and TV (the height or width)? Calculate y.


Calculate width and height and area of image?




Calculate percent of area. (Percent Area= area of image/area of TV *100)



Calculate width black bar. ((height of TV – height of image)/2)



Calculate area of black bar.

Answer 1

A)

(16x)^2 + (9x)^2 = 72^2

256x^2 + 81x^2 = 5184

337x^2 = 5184

337x^2 / 337 = 5184 /337

x^2 = 15.383

x = √15.383

x = 3.92

B)

Height = 9x = 9(3.92) = 35.28 inches

Width = 16x = 16(3.92) = 62.72 inches.

Area = 35.28 x 62.72 = 2212.76 in^2

C)

The width. Y =  height = width / ratio = 62.72 / 1.95 = 32.16 inches.

D) Height = 32.16 inches ( from C) , Width  = 62.72 inches.

Area = 32.16 x 62.72 = 2017.08 in^2

E) 2017.08 / 2212.76 = 0.9115 x 100 = 91.16%

F) 35.28 - 32.16 = 3.12 / 2 = 1.56 inches.

G) 1.56 x 62.72 = 97.84 in^2