It is possible only if you make some assumptions that are not stated in the problem.
It is possible only if you make some assumptions that are not stated in the problem.
Are AB and DE parallel?
Is CDE isosceles?
Given that, I can answer your question: Yes, it is possible.Yes, parallel and isoceles.
Thanks.
Beat me to it!Given that, I can answer your question: Yes, it is possible.
Now, if you really want the solution, not just a yes/no, you'll need to follow the guidelines! (See #2.)
What have you tried? Where are you stuck?
I can tell you that I worked with just one half of the figure, and some right triangles.
This is key. Hint: imagine line AB moving up and down vertically. This will affect the lengths of FG and AB differently (one increases as the other decreases). Therefore, you need to use the given equation "FG = AB/5" to lock in the height of DEGF....get the height of DEGF.
Since angles FDE and GED are equal we get FD = EG. (If you drop a height from F to DE (which is the same h from G to DE) then etc.)@Cubist
I still do not get it. Did you assume that DF is the same length as EG?
As I understand it, that is not a given.
The first thing I did was to construct an approximate figure, without assuming an isosceles triangle, to confirm that was necessary for the answer to be constant; in doing so, I used exactly this idea, moving FG up and down.This is key. Hint: imagine line AB moving up and down vertically. This will affect the lengths of FG and AB differently (one increases as the other decreases). Therefore, you need to use the given equation "FG = AB/5" to lock in the height of DEGF.
Given the assumptions we've elicited, the entire figure is symmetrical.@Cubist
I still do not get it. Did you assume that DF is the same length as EG?
As I understand it, that is not a given.