Question

if x is the length of side of an equilateral triangle find its area​

Answer 1

Answer:

Consider an equilateral triangle ABC having sides a and a median AD of length x unit'.

In an equilateral triangle, the median is always the perpendicular bisector of the triangle.  

So, BD=a/2

In triangle ABD, by pythagoras theorem, we have

AB  

2

=AD  

2

+BD  

2

 

⟹a  

2

=x  

2

+(  

2

a

​  

)  

2

 

⟹a  

2

=x  

2

+  

4

a  

2

 

​  

 

⟹  

4

3a  

2

 

​  

=x  

2

or,a  

2

=  

3

4x  

2

 

​  

 

Now, area of equilateral triangle =  

4

3

​  

a  

2

 

​  

=  

4

3

​  

 

​  

×  

3

4x  

2

 

​  

=  

3

3

​  

x  

2

 

​  

 

solution

Step-by-step explanation:

Answer 2

Answer:

√3×x^2/4

Step-by-step explanation:

length=x

area of equilateral triangle= √3×(side)^2/4.

according to question

area= √3×x^2/4