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).
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 = 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)