SOLUTION: A square, an equilateral triangle and a circle all have the same perimeter. Which one has the largest area?

Question 1209549: A square, an equilateral triangle and a circle all have the same perimeter. Which one has the largest area?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: Circle

Explanation:
Check out this similar question
https://www.algebra.com/algebra/homework/formulas/Geometric_formulas.faq.question.1209550.html
That question involves a farmer having 114 feet of fencing to make various shaped enclosures. The circle offered the largest area. Feel free to change the 114 feet to some other number, and you'll find the circle is always the winner.

Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

Alternatively or in addition, you may read this Internet article

https://www.quora.com/A-circle-a-square-and-an-equilateral-triangle-have-equal-perimeter-Which-figure-will-contain-maximum-are

It contains a detailed discussion with formulas and numbers
for any shape you listed in your post.

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