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## Homework Statement

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Hello!

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**

2. 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.