Question

Determine the dimensions of the screen of a 42-inch TV with a 4:3 aspect ratio.

Hint: Use 3x^2+4x^2=42^2 to help.

Answer 1

Aspect ratio is the ratio of the width to the height.

So if we let the unknown scale factor be called s ,

then the width = 4s

and the height = 3s

Now we can use the Pythagorean Theorem to find what s is.

(4s)2 + (3s)2 = 422 This is the equation given in the hint.

(4s)(4s) + (3s)(3s) = 422

16s2 + 9s2 = 422

Just like 16 apples + 9 apples = 25 apples, so does 16s2 + 9s2 = 25s2

25s2 = 422

Let's rewrite 25s2 like this...

(5s)2 = 422

and take the square root of both sides.

5s = 42

s = 8.4 (inches)

Now that we know what s is, we can find the width and the height.

width = 4s = 4(8.4) = 33.6 (inches)

height = 3s = 3(8.4) = 25.2 (inches)

Explanation:

Answer 2

For this case, the first thing you should do is know that the measurement of a television is given by the diagonal of the television.

Therefore, to find the value of x, we use the Pythagorean theorem.

We have then:

`(3x)^2+(4x)^2=42^2`

Rewriting we have:

`25x ^ 2 = 1764\\x = \sqrt {\frac {1764} {25}}\\x = \sqrt {70.59}\\x = 8.4`

Then the dimensions are given by:

`4x = (4 * 8.4) = 33.6\\3x = (3 * 8.4) = 25.2`

Answer:

the dimensions of the screen are: 33.6* 25.2