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anonymous
 5 years ago
The ratio of the lengths of two equilateral triangles is 4:9. what is the ratio of their areas?
anonymous
 5 years ago
The ratio of the lengths of two equilateral triangles is 4:9. what is the ratio of their areas?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Lets see if the area of triangles are ratioed as well. 34. 3*4 = 12/2 = 6 are of 34 is 6 triple the side 91215; 9*12 = 108/2 = 54 but 6*3 is not 54, so we cant assume that the areas are of equal ration to the sides...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04^2 = h^2 + 2^2 16  4 = h^2 12 = h^2 h = 2sqrt(3); b=4/2 Area of 4sides equilateral Triangle is 4sqrt(3) 9^2 = h^2 + 4.5^2 81  20.25 = h^2 60.75 = h^2 h = sqrt(60.75) = 2sqrt(15) the ration of the areas is 4sqrt(3) : 2sqrt(15) if I havent tripped over myself :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, I tripped alright...let me try finishing that up alittle :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0h/2 times 9 The Area of the 9side Triangle is: 9sqrt(15) We got a ratio of 4sqrt(3) : 9sqrt(15).....maybe :)

radar
 5 years ago
Best ResponseYou've already chosen the best response.0This is obviously confusing. The area of a triangle is given as A=1/2bh where base would be one side but the heights h would also be related to the lenght of the side. In a equilateral triangle, what would that relationship be? Without a diagram you have to imagine the height as h=sqrt(b^2(b/2)^2)

radar
 5 years ago
Best ResponseYou've already chosen the best response.0\[h=\sqrt{b ^{2}(b/2)^{2}}\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0So Area expressed in terms of its base (which is a side) would be: \[A=1/2b(\sqrt{b ^{2}(b/2)^{2}}\] I need to think this further. I'll be back

radar
 5 years ago
Best ResponseYou've already chosen the best response.0After doing some more ciphering! The above works out to be:\[A=(b ^{2}\sqrt{3})\div4\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0substituting 4 and then substituting 9 shows a ratio between areas 1:5 I am not comfortable with this answer, hopefully you will get the school solution and post it here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the answers i have are 4:9, 9:4, 2:3, 16:81, and 81:16

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Hey DavisAshkey it looks like you came up with the proportion squared, or the square root of the proportion of the sides. You very well may be correct. I will look at it again. The squared version looks reasonable!
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