Question

You have just bought a new television and it has an aspect ratio of 16:9. The screen on the television is 65 inches. What is the width, height, and area of the television?

Answer 1

w = 56.65 in; h = 31.87 in; A = 1805 in²

Explanation:

The aspect ratio of 16:9 tells us that w:h = 16:9 .

Let w = 16x and h = 9x.

The 65 in measurement is the diagonal length of the screen.

According to Pythagoras,

( 16x)² + (9x)² = 65²

256x² + 81x² = 4225 Combine like terms

337x² = 4225 Divide each side by 337

x² = 12.54 Take the square root of each side

x = 3.541 in

w = 16 × 3.541

w = 56.65 in

h = 9 × 3.541

h = 31.87 in

A = wh

A = 56.65 × 31.87

A = 1805 in²

Answer 2

Width of T.V. is 21.94 inches Height is 39 inches and area is 855.66 square inch.

Explanation:

When we buy an electronic item like T.V or Blue Ray aspect ratio is the term which is used by the salesmen or technicians. Aspect ratio is actually the ratio of length and breadth of the screen of a device or ration of width and height.

In this question aspect ratio of television is given as 16:9

This can be written as
`(W)/(H)=(16)/(9)` or
`W=(16)/(9) H`

Screen of the T.V. is 65 inch which is the diagonal length of the screen.

We know from pythagoras theorem in a right angle triangle

`(diagonal)^(2)=(base)^2+(height)^2`

`(65)^2=(Base)^2+(height)^2`

`(65)^2= W^2+H^2 = ((16)/(9)H)^2+H^2`

`(65)= \sqrt{(16)/(9)H^2+H^2}\\ 65=H\sqrt{(16)/(9)+1}\\ 65=H\sqrt{(25)/(9)}\\ 65=(5)/(3)H\\ H=39 inches`

Now height of the T.V.will be

`(W)/(H)=(16)/(9) \\\\(H)/(W)=(9)/(16)\\ H=(9)/(16)W = ((9)/(16))39= 21.94 Inches`

now area of the T.V.=W×H=39×21.94=855.66 square inch