Question

from A point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. the lengths of the perpendiculars are 14 cm, 10 cm, 6 cm. find the area of the triangle.​

Answer 1

Answer:

Correct option is B)

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

​

㎠

Step-by-step explanation: