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Vijay Sharma

· started a discussion

· 1 Months ago

KNOWLEDGE EXPERT ARE U DUMB...SO MANY PEOPLE HAVE REPORTED (Question:117234.0)

Why dont you pick pen and paper to check when people are telling you thats answer is wrong...

considering outermost square...

find BC ; BC = √{a^2/4 + a ^2/4) = a/√2

for radius BC / 2 = a/2√2

radius = circumradius of triange

a/2√2 = s/√3 (here s is side of triangle)

√3a/2√2

area = √3/4 × √3/2√2 × √3/2√2 = 3√3a²/32

Question:
What is the area of the inner equilateral triangle if the side of the outermost square is ‘a’? (ABCD is a square).

Options:
A) \(\cfrac{3\sqrt[]{3}a^2}{32}\)
B) \(\cfrac{\sqrt[]{3}a^2}{16}\)
C) \(\cfrac{5\sqrt[]{3}a^2}{32}\)
D) \(\cfrac{5\sqrt[]{3}a^2}{64}\)
Solution:
Ans: (b) \(BD=a,EF=\cfrac{a}{2}\)

\(\therefore\) area of equilateral triangle EFG \(=\cfrac{\sqrt[]{3}}{4}\left ( \cfrac {a}{2} \right )^2=\cfrac{\sqrt[]{3}a^2}{16}\)

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