a television has a 50in diagonal screen if the aspect ratio

a television has a 50-in. diagonal screen. if the aspect ratio (length to width) is 1.6 to 1, determine the length and width of the screen. round to one decimal place.

Solution

Let the width be x inch

So, length = 1.6x inch

diagonal = 50 inch

According to pythagoras theorem,

length² + breadth² = diagonal²

or, (1.6x)² + x² = 50²

or, 2.56 x² + x² = 2500

or, 3.56 x² = 2500

or, x² = 2500 / 3.56

or, x = 26.5

Width = 26.5 inch

So, length = 26.5 * 1.6 = 42.4 inch