Question

From a point in the interior of an equilateral triangle perpendiculars are drawn on 3 sides. The l of perpendiculars = 14 cm, 10 cm and 6 cm. Find area

Answer 1

if a line is drawn from the point to the vertices than we get a set of3 right angled triangles .

let the first Side be x+z and its opp.side be y +r and third side be m+n.

x^2+14^2=y^2+10^2

x^2-y^2= -96

similarly,

z^2-m^2=-160

n^2-z^2=

Answer 2

let the sides of equilateral triangle be a

now if we divide the triangle from the point to the vertices

we get three triangle

now

area of 1st triangle= 14/2 × a

                             = 7a

area of 2nd triangle= 10/2 × a

                             = 5a

area of 3rd triangle= 6/2 × a

                             = 3a

total area = 15a

now we know

area of  equilateral triangle =√3/4a²

15a = √3/4a²

15×4/√3=a

a = 5√3

again

area of  equilateral triangle =√3/4a²

                                              =√3/4(5√3)²

                                             75√3/4 cm²