Question

Another geometry question!!

Answer 1

is the answer 6 ?

Answer 2

It's 12

Answer 3

Ahh right!

Answer 4

I am sure that DEF/(DBF + EFC) = 1/2

Answer 5

where did 2:3 come from?

Answer 6

one sec, there is a mistake... let me think a bit

Answer 7

is it 2:3 or 4:9?

Answer 8

Exactly! medians are in ratio 2:3, therefore areas will be in ratio 4:9

Answer 9

I solved it on my book. but it is not very clear. I will post it

Answer 10

okay waiting :)

Answer 11

thats very neat ! im gona delete my mess...

Answer 12

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

Answer 13

To be honest, I went back from the answer to the question:). But it works.

Answer 14

@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?

Answer 15

Well, Yes. I argue that altitude is proportional to the median as they extruded. doesn't is?

Answer 16

Yes, if the triangles are similar, all lengths(medians, altutudes, perimeters etc) will be proportional..

Answer 17

so I don't really see a problem hmm ...

Answer 18

Hey are you assuming DE is half of BC ?

Answer 19

That appears to be the assumption, which is not mathematics