Question 1009282: I am very stuck. I can't figure out how to solve this. I know it involves pythagorean theorem, but I don't know how to solve it without legs. Can you help me, please?
There are two tvs of different sizes. One is a 42" diagonal TV that costs $420, the other is a 50" diagonal tv that costs $550. The aspect ratio of each is 16:9, width to height. What is the cost per square inch of each tv?
Thank you in advance!
Found 2 solutions by fractalier, stanbon:
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! For the larger TV, we can call the legs 16x and 9x. Then like you said, using the Pythagorean Theorem, we have
a^2 + b^2 = c^2
(16x)^2 + (9x)^2 = 50^2
256x^2 + 81x^2 = 2500
337x^2 = 2500
x^2 = 2500/337 = 7.4184
x = 2.724
Then we can multiply that factor by 16 and 9 to get the dimensions of the larger TV and get
16(2.724) = 43.584
9(2.724) = 24.516
To find the area, we multiply these and get
A = LW = 1068.5 in^2
Divide $550 by that and get
$0.5147 per square inch.
Now repeat that exact same procedure, using the smaller TV.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! There are two tvs of different sizes. One is a 42" diagonal TV that costs $420, the other is a 50" diagonal tv that costs $550. The aspect ratio of each is 16:9, width to height. What is the cost per square inch of each tv?
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Note:: 16:9 is the same as 16x:9x
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Equation for 42" TV::
sqrt[(16x)^2+(9x)^2] = 42
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(16x)^2 + (9x)^2 = 42^2
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337x^2 = 1764
x^2 = 5.2344
x = 2.287
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Dimensions::
9x = 20.59"
16x = 29.73"
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Area = 612.16 sq in
Cost per square in:: $420/612.16 = $0.69
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I'll leave the 2nd TV cost per square in to you.
Cheers,
Stan H.
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