Given a rectangle ABCD with |AB|=a and |BC|=b.
There are two distinct equilateral triangles AEF
and AGH with points E and G on line BC and points
F and H on line CD. What is the product of the areas
of the two triangles in terms of a and b?
Hey Bractals, I don't understand the wording of this problem. Is the second sentance supposed to follow from the first? As far as I can tell, and arbitrary rectangle doesn't imply any inscribed equilateral triangles with vertices at A, let alone two.
In fact, I would argue that two distinct equilateral triangles under the stated conditions is impossible (though my reasoning is geometric, and doesn't translate easily to html).
By line BC do you mean the line conatining B and C or the line segment BC? I would guess that using the infinite lines containing BC and CD, two distinct triangles can be found, but i'm too tired to prove it tonight. I'll give it a shot tomorrow, if no one beats me to it.
huh?
