Question

What are the actual dimensions of a television that has a 15:9 aspect ratio and a screen that is 42 inches?

Answer 1

Let x be the number.

It is given that a 15 : 9 aspect ratio and a screen that is 42 inches.

Aspect ratio states that the ratio of the display image’s width to its height.

Then;

Width of the television of(w) = 15x

and

height of the television(h) = 9x.

Since, television is in the form of Rectangle.

and it is also, given that the screen is 42 inches .

⇒Diagonal of the television(D) = 42 inches

Using formula of diagonal of the rectangle :

`D^2 =w^2+h^2`

Substitute the given values to solve for x;

`42^2 = (15x)^2+(9x)^2`

`1764 = 225x^2 + 81x^2 = 306x^2`

or

`x^2 = (1764)/(306) = 5.76`

`x = √(5.76) = 2.4`

Then:

width of the television (15x) = 15(2.4) = 36 inches and

Height of the television (9x) = 9(2.4) = 21.6 inches.

Therefore, the actual dimensions of the television are;

width = 36 inches and height = 21.6 inches.