concentric rectangles
Given that
A
=
1
0
,
B
=
2
0
and
C
=
5
, what is the length of
D
?
The answer is 19.4.
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2 solutions
[Nevermind this solution.I misread the problem(But still got it right?So lucky)]
The diagonal of the smaller rectangle = 2 0 2 + ( 1 0 − 5 − 5 ) 2 = 2 0 ,so D = 2 0 2 − 5 2 = 3 7 5 ≈ 1 9 . 4
sorry but it seems to me that you just got lucky... in fact i didn't understand your solution and i dont think it works for other values... can you try for the following examples...? (A=1234; B=5678; C=910; D=5634,86 (not 5573,9)) or (A=4321; B=8765; C=19; D=9757,17 (not 7647,3))...if you try it with some CAD software that allows parametrization you can check it...any way, I'll soon post what i consider to be a reasonable algebric solution and hope for you to share your comments...thank you.
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D = B 2 + ( A − 2 C ) 2 − C 2
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So..., it seems to me that there is a miss understanding about the picture because the measure “C” is not parallel to the measure “A”. In this case, your formula works as a good approximation. But if you plug in some big numbers the error will become noticeable. Let’s try some other values: A=98765 ; B=123456 ; C=45678 ... ((123456^2)+((98765-2*45678)^2)-( 45678^2))^(1/2)=114933,88 instead of 116465,17 that would be the exact value...
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@Nordau Luiz Palko Roberto Santos – Yeah,you're right.I misunderstood it as A//C.