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.
<h3>Diagonal units</h3>
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.
<h3>Screen dimensions</h3>
The width is ...
(4/5)(47 in) = 37.6 in . . . width
The height is ...
(3/5)(47 in) = 28.2 in . . . height
<h3>Area</h3>
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.
