Question

Given an equilateral triangle, the length of perpendiculars drawn from a point in the

interior of a triangle to the three sides are 6cm, 10cm, 14cm. Find the area of the triangle.​

Answer 1

Let each side of ㎝ equilateral triangle ABC be

′

a

′

㎝

Now, ar△OAB=

2

1

×AB×OP=

2

1

×a×14=7a㎠→1

ar△OBC=

×BC×OQ

=

2

1

×a×10=5a㎠→2

ar△OAC=

2

1

×AC×OR=

2

1

×a×6=3a㎠→3

∴ar△ABC=1+2+3=7a+5a+3a=15a㎠

Also area of equilateral triangle ABC=

4

3

a

2

Now,

4

3

a

2

=15a⇒a=

3

15×4

×

3

3

=

3

60

3

=20

3

㎝

Now, ar△ABC=

4

3

×(20

3

)

2

=300

3

㎠