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

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Answer 1 · 2018-05-13T14:45:41

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

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#