At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
is the answer 6 ?
I am sure that DEF/(DBF + EFC) = 1/2
where did 2:3 come from?
one sec, there is a mistake... let me think a bit
is it 2:3 or 4:9?
Exactly! medians are in ratio 2:3, therefore areas will be in ratio 4:9
I solved it on my book. but it is not very clear. I will post it
okay waiting :)
thats very neat ! im gona delete my mess...
explanation, 1.height of both triangles proportional to the line through center of gravity. so as the line(center of gravity on) expand , height also expand by 3/2 2. based on my observation, DE becomes double when it goes to BC 3. so if you take the ratio between ADE : ABC = 3 4. then we can say ADE = 54/3 = 18 5. And DEBC = ABC - ADE = 54 - 18 = 36 6. As said earlier DEX = DEBC/3 by obervations 7 . DEX = 36/3 = 12
To be honest, I went back from the answer to the question:). But it works.
@ganeshie8 But the problem with my solution is that it doesn't obey the ratio 9:4. Because DE becomes double. not 3/2DE like the height. so the ratio between ADE and ABC would be 1:3. which is kind of strange to me. Do you have any thoughts on that?
Well, Yes. I argue that altitude is proportional to the median as they extruded. doesn't is?
Yes, if the triangles are similar, all lengths(medians, altutudes, perimeters etc) will be proportional..
so I don't really see a problem hmm ...
Hey are you assuming DE is half of BC ?
That appears to be the assumption, which is not mathematics