Question

Find the width and heigth of a newer 47-inch television whose screen has an aspect ratio of 4:3

Answer 1

Answer:

• width: 37.6 in
• height: 28.2 in
• area: 1060.32 in²

Step-by-step explanation:

The measurement used to describe a television is the length of its diagonal. The relation between the width, height, and diagonal is described by the Pythagorean theorem.

Diagonal units

The Pythagorean theorem tells us the relation between the sides of a right triangle and its hypotenuse. The diagonal of a rectangle is the hypotenuse of a right triangle whose sides are the width and height of the rectangle. If 'c' is the number of "ratio units" in the diagonal, we have ...

  4² +3² = c²

  c = √(16 +9) = 5

The diagonal of the screen is 5 ratio units, so the width is 4/5 of the length of the diagonal, and the height is 3/5 the length of the diagonal.

Screen dimensions

The width is ...

  (4/5)(47 in) = 37.6 in . . . width

The height is ...

  (3/5)(47 in) = 28.2 in . . . height

Area

The area is the product of the width and height:

  A = WH = (37.6 in)(28.2 in) = 1060.32 in²

The area of the screen is 1060.32 square inches.