Question

A triangle has one side 6cm and the sum of other two sides is 10cm.Find the maximum possible area of the triangle.

Answer 1

owing to the symmetry , either 6,6,4 should have max area of 5,5,6

am just saying,,anyone would like to confirm ?

Answer 2

or* 5,5,6

Answer 3

try heron's formula .. maximize it

Answer 4

this can also be viewed as :
the sum of sides is constant , so the fixed points are the focii of an ellipse where distance between the focii = 6
and sum of distances from focii to circumference is 10

clearly area is max when other side is at the edge of minor axis..

Answer 5

other point* is at the edge of minor axis

Answer 6

http://www.wolframalpha.com/input/?i=maximize+sqrt%288+*+2*+%288-x%29%288-%2810-x%29%29

Answer 7

allow me to put in other words,
let P be a point on the ellipse,


area = 1/2 (height)(6) = 3 height

more the height, more the area
height is ofcorse max at the minor axis end,and hence your ans, knowledge of eqn of ellipse , or anything legit will allow you to calculate length of minor axis and hence every other required detail..

Answer 8

but this area is of right angle

Answer 9

area = 1/2 hb