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

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

Answer 2

Answer:

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)

Step-by-step explanation: