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2 years ago

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

Mathematics

1 answer:

LuckyWell [14K]2 years ago

8 0

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

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.

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