[Solved] Maximise this triangle's area ¬ Geometry Challenge  

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Very nice question involving some geometry and calculus- plenty of room for mistakes!

An isosceles triangle has two equal sides of length "x". For a fixed perimeter "p" find the value of x (in terms of p) which maximizes the triangle's area. Also find all the angles in this triangle.

Solution will be up later this week 🙂

PlanckTime - Amin

 
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Good q - the area will be maximised when it's an equilateral triangle so when x=p/3 & all the angles are 60 degrees. I think this works as a proof but I've got an extra bracket in the derivative which probs shouldn't be there but cba to sort it out 😉

 
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Good stuff Beth, you shouldn't have a second bracket, the two similar brackets after differentiating multiply to cancel one out as shown in our solution. Hopefully it clarifies it!

Your answer came out correct though, I'm intrigued as to why!

PlanckTime - Amin

 
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