Answer:
- width: 37.6 in
- height: 28.2 in
- area: 1060.32 in²
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.