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aditya

· started a discussion

· 1 Months ago

soln (Question: 108713.0 )

if side of eqilateral triangle is a then circum radius is = side/root(3)

area of equilatel triangle = [ root(3)/4] * a^2

area of circumcirle = pie( a/root(3)) ^2

after comparing 3 root(3) : 4 pie

Question:

What will be the ratio of the area of the equilateral triangle to the area of its circum circle?

Options:
A) 1 : 2
B) \(\sqrt[]{3}\) : 2
C) \(\sqrt[]{3}\) : 4
D) None of these 
Solution:
Ans: (d) Let the side of an equilateral triangle be ‘a’.

Radius of the circum circle = \(\cfrac{a^3}{4\triangle}\)

(Where \(\triangle\) is the area of the triangle)

Now, area of the circum circle = \(\pi \left ( \cfrac{a^3}{4\triangle} \right )^2\)

Area of equilateral triangle = \(\cfrac{\sqrt[]{3}}{4}a^2\)

Required Ratio = 


Knowledge Expert

· commented

· 1 Months ago

Dear Student,
Your method is also correct.

Thanks and Regards
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