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 you find the dimensions).

Guest Sep 3, 2019

edited by
Guest
Sep 3, 2019

#1**+1 **

It is a 42-inch TV. This means the length of the diagonal is 42 inches.

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} = 42^{2} This is the equation given in the hint.

(4s)(4s) + (3s)(3s) = 42^{2}

16s^{2} + 9s^{2} = 42^{2}

Just like 16 apples + 9 apples = 25 apples, so does 16s^{2} + 9s^{2} = 25s^{2}

25s^{2} = 42^{2}

Let's rewrite 25s^{2} like this...

(5s)^{2} = 42^{2}

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)

hectictar Sep 3, 2019