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anonymous
 4 years ago
Need help with Geometry and Ratio Question!! Please Help!!
anonymous
 4 years ago
Need help with Geometry and Ratio Question!! Please Help!!

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The base of a triangular piece of paper ABC is 12 cm long. The paper is folded down over the base, with crease DE parallel to the base of the paper. The area of the triangle that projects below the base is 16% that of the area of the triangle ABC. What is the length of DE, in cm.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327792772445:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327793675334:dw ok so we actually are interested in the area of the triangle CFG too, since that is the one that projects below the base.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0What is the connection between those triangles?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0These are similar triangles. There exists a scale factor s>1 such that \[ABC = s^2CFG.\] Another fact about s is that \[FGs = AB = 12\] Therefore \[s = \frac{12}{FG}.\] There also exists another scale factor, r>1 such that \[ABC=r^2CDE\] and obviously another fact about r is that \[rDE = AB = 12\] Therefore \[r=\frac{12}{DE}\] We are also told that the area of the triangle that projects below the base is 16% that of the area of the triangle ABC. So we get \[0.16ABC = CFG.\] What I think we should do is solve for r solve for s and then solve for DE.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i understand that they are similar but I don't quite understand why is (s^2)(CFG)=ABC. Why does s have to be squared?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is it some sort of formula?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[0.16s^2CFG = CFG \Longrightarrow s=\sqrt{\frac{1}{0.16}} = 2.5\] Also, \[s=\frac{12}{FG} \Longrightarrow FG = 4.8\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well similar lengths are scaled by a factor, and similar areas are scaled by the square of that factor

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so we have found s, maybe try to find r next

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so does it work the same for r too?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327795417846:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0r is a little more tricky...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0because we don't know what percent is CDE of ABC

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0actually no... \[(0.4)^2 ABh_1 = FGh_2\] So it must be that \[0.4h_1 = h_2\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes, but what about CED?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah, we need to try to figure out something relating s and CDE so we can use \[ABC = r^2CDE\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'm going to think about it for a bit lol

phi
 4 years ago
Best ResponseYou've already chosen the best response.2If you want a hint. I hope this is not too cryptic

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Can you clarify ? dw:1327797362393:dw

phi
 4 years ago
Best ResponseYou've already chosen the best response.20.4 you figured that out up top. It is the ratio of altitudes of 2 similar triangles. When the areas are in the ratio of 0.16/1 the altitudes are in the ratio sqrt(.16)/sqrt(1)= 0.4= 2/5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah phi that's excellent, 0.4 is the scale factor for the heights of the triangles I had above: \[0.4h_1 = h_2\] and yeah r is the ratio of the heights of CDE and ABC. Thanks phi
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