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Q.

Each side of an equilateral triangle is equal to the radius of a circle whose area is 154  cm 2  . The area of the triangle is:


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a

7 3 4   cm 2  

b

49 3 2 cm 2  

c

49 3 4   cm 2  

d

7 3 2   cm 2   

answer is C.

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Detailed Solution

Given that each side of an equilateral triangle is equal to the radius of a circle whose area is 154  cm 2  .
Area of circle formula is,
A=π r 2  
Substituting given area in above formula to get radius.
Question Image ⇒r= 154×7 22  
⇒r=7cm  
Area of equilateral triangle with side length a is,
A= a 2 3 4  
As the radius of circle is equal to side of the triangle, then area of triangle is,
⇒A= 7 2 3 4  
⇒A= 49 3 4 c m 2   Therefore, the area of the triangle is 49 3 4 c m 2  .
Hence, option 3 is correct.
 
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