Question

From a point in the interior of a equilateral triangle, perpendiculars are drawn on the three sides. the lengths of the perpendiculars are 14cm, 10cm and 6cm. find the area of triangle. (please answer step by step) most worthy answer will be marked brainliest.​

Answer 1

Answer:

Step-by-step explanation:

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

​

㎠