Question

a point o is taken inside an equilateral triangle abc. if ol is perpendicular to bc, om is perpendicular to ac and on perpendicular to ab such that ol is equal to to 14cm mm is equal to 10 cm and on is equal to 6 cm find the area of triangle abc

Answer 1

Answer:

15a cm (where a is the side of triangle)

Step-by-step explanation:

Let o be the point inside a triangle abc

Let a be the side of equilateral triangle abc

given,

ol= 14 cm

om= 10 cm

mn= 6 cm

Now draw lines from a to o, b to o and c to o

Now we see that,

Δabc= Δaob+Δboc+Δaoc

area of Δabc= sum of areas of Δaob+Δboc+Δaoc

area of Δaob= 0.5×a×6= 3a

area of Δboc= 0.5×a×14= 7a

area of Δaoc= 0.5×a×10= 5a

total area= 15a

area of Δabc= 15a