SOLUTION: So my friend tells me that if I buy a 16:9 HDTV, I need to consider how big the picutre will be when it displays a 4:3 (standard TV) picutre. I know that 16:9 = 1.78 (rounded) and

Question 44938: So my friend tells me that if I buy a 16:9 HDTV, I need to consider how big the picutre will be when it displays a 4:3 (standard TV) picutre. I know that 16:9 = 1.78 (rounded) and 4:3 = 1.33 (rounded). I know that 1.78/1.33 is about 1.33. That tells me that the picture length will be 33% shorter at 4:3 than 16:9. But the question is: what is the length at 16:9? I'm only given the diagonal, because that's what they give for specs. So I came up with these equations (where b & a are length & height, respectively):
a^2 + b^2 = 42 inches (thank you, Pythagoras)
b/a = 1.78
16a - 9b = 0
Given my goal, are these equations helpful to answering my question? And if so, how do you solve for a and b? I remember how to solve linear equations, but not when expoenets are involved. If I could somehow take the square root of the pythagorean equation... but I know it doesn't work that way.
How 'bout a lil help? Take me back to Mr. Anderson's classroom... :-)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You have a 16:9 rectangle with a diagonal of 42"
The sides are in a ratio of 16x:9x
Using Pythagoras you have the following:
(16x^2) + (9x^2) = 42^2
337x^2 = 1764
x^2= 5.234
x=2.878
Your length is 16x = 36.61 inches
Your width is 9x=20.59 inches.
Cheers,
Stan H.
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