I have this question which I don't quite know how to solve...
ABC is an equilateral triangle - the length of its sides equal to (a).
DE is parallel to BC
1. What length should DE be to achieve the largest possible area of triangle BDE?
2. What length should DE be to achieve the smallest possible perimeter of triangle BDE?
How should this be done (step-by-step, my knowledge of math is quite basic)?
The attempt at a solution
I tried to solve the first question and got that DE should be (a/2) to make the maximum area of BDE. (I let DE = (a-a/x) and BD = (a/x), I used a formula to calculate area of a triangle using 2 sides and the angle between (120°) and then I derived the area expression...
But I think that what I was attempting is very messy, and I am unsure if the way I did it is correct.
Also, I didn't manage to solve the second question about the perimeter.
If anyone could explain and show the correct answer for comparison, I would be very grateful.