Question

The perimeter of a triangle is 7 cm. What is its greatest possible area?

Answer 1

`(49sqrt(3))/36\ "cm"^2`

Explanation:

For same perimeter among different types of triangle, equilateral triangles have maximum area.

Therefore, length of each side of triangle`= "7 cm"/3`

Area of equilateral triangle is

`"A" = sqrt(3)/4 × ("side length")^2`

`"A" = sqrt(3)/4 × ("7 cm"/3)^2 = (49sqrt(3))/36\ "cm"^2`

[Simple proof that equilateral triangles have maximum area.](https://math.stackexchange.com/questions/592917/simple-proof-that-equilateral-triangles-have-maximum-area)