1remove 'also' in 1st line...
26 Answers
1assume any point on any median;take its diatance from corner=x and proceed;
xsin30+xsin30+(√3-x)=√3;
so any point on mediands will satisfy;
check for corners, it will also satisfy;
checking for arbitrary is ur duty,i have done enough work:)
1ya numericalllyyy also it will not b equal to area(not always i meant);
as area of tr. will depend on base leght,altitude.
but sum of distances =altitude(always for an equi. tr.)
33ufff.......
by eq to areaa i meant..
sum of distances is comin equal numeraically to area of triangle...
1yes it is true for any eqiulaterAL triangle.
and what du u mean by here equal to area of triangle;
when all smaall smalllll points satisfy then they will paint the whole triangle...
understood.....
33@ mkagenius..
we are having prob in visulaising that why all points satisfy not where area is formed...
itna eqn likh kar to gadha bhi bana dega.. (jada ho gaya)
sorryyyy...
was kiddin.. :P
33So it is general for any equilatral Δ [7]
sum of three dis from any pt inside to the sides is same... here eq to area also...
kitna acha ho ki sare Δ me ho.... par i don think it is true for others...
1although points dont have area but if there are infinite no of points closely(rather adjacently)
placed it will result in area.
this is what is asked ,i think.
as all points satisfy the given condition...
then why u guys have problem in visualising ...i am not understanding.
62This was my hunch too.. but it did not seem obvious to me
bcos all the three vertices satisfied this condition..
The physical proof still does not seem very obvious to me :(
11how can it be visualized when u r considering the sum of three distances u r not considering a single distance
i hope it makes some sense
33eqns of the sides are
y=0
y=√3x
y=-√3x+2√3
now
let pt(x,y) be the interior pt.
|y|+|y-√3x| + |y+√3x-2√3| = √3
2 2
now as pt is interior therefore removing | | appropriately...
2y-(y-√3x)-(y+√3x-2√3)=2√3
it gives 0=0
so all interior pts satisfies ... [11]
so area is area of Δ i.e. √3
But one problem if it is whole Δ it should have been physically visualized... [2]
1GENIUS.....
WELL DONE DUDE....
CAN V HAV AN ALGEBRAIC PROOF FOR ANY ARBITRARY PT JUS LIKE U SHOWED FOR PTS. ON MEDIANS???
FOR MCQ's UR WAY OF SOLVING IS PERFECT!!!!
THNX A LOT GENIUS....
11the area within which all the points satisfy the givven condition i think so
i could only find that the incentre satisfied this condition
1although points dont have area but if there are infinite no of points closely(rather adjacently)
placed it will result in area.
this is what is asked ,i think.
1Why don't we try complex numbers ?? Excuse me if its wrong or too wild :D , tell me something , what does it mean actually ?? Area of the region representing all possible positions of the point P . Which region ?
1i think for all points inside that triangle ,the given condition is true;
although i checked only for the perpendicular bisectors;
sum of distances of any point from any bisector=√3;
also it is true for all A,B,C;
1well . I thought like this , it's an equilateral triangle .
so to get a point which is equidistant from all sides is the centroid only , then the dist from one side is root 3 / 2 , so I thought it's none. whats wrong?please batao .
1HA HA WAT A WILD GUESS.....
NOW LET ME DISCLOSE DA ANSWER COZ TWO OF THEM HAV BN NEGATED!!!!
ANS IS C √3 SQ UNITS.....
1ek bekar saa method...
do all those traditional things...
but it will be toooooooooo lengthy [2]
kuchh achha wala method sochte hai...
