A old tube TV has a screen ratio of Height to Width 34 That

A old tube TV has a screen ratio of Height to Width 3:4. That is for every 3 inches in height, the screen will have 4 inches of wididth. What are the dimensions of the Old Tube whose advertised diagonal is 56 inches. Round answers to nearst 10th.

Height = ?? inches

width = ?? inches

Solution

Let the height of the TV screen be 3x. Then, its width is 4x. Since the diagonal of the old tube bakes a right angled triangle with the height and the width, as per Pythegoras theorem, the square of the diagonal (hypotenuse) is the sum of the squares ot the height and the width. That is ( 56)² = (3x)² + (4x)² or, (56)² = 9x² + 16x² or 25x² = (56)² or, (5x)²   = (56)² . Therefore 5x = 56. Then x = 56/5 = 11.2. Therefore

Height = 3x = 3(11.2) = 33.6 inches

Width = 4(11.2) = 48.8 inches