The diagonal of a square is twice the side of equilateral triangle the ratio of Area of the Triangle to the Area of Square is?
a) √3:8 b) √2:5 c) √3:6 d) √2:4

• let side of square is a
  then diagonal of square is {sqrt2a}
  given {sqrt2a}= 2*side of triangle
  so side of triangle = {sqrt2a}/2 i.e a/sqrt2
  area of triangle = sqrt3/4*side^2......according to formula
  new area = sqrt3/4*{a/sqrt2}*{a/sqrt2} i.e.........sqrt3a*a/8
  area of square = a^2
  ratio = sqrt3*a^2/8a^2....i.e sqrt3/8
• 11 years agoHelpfull: Yes(55) No(3)
• is it 2012 tcs recent paper???
• 11 years agoHelpfull: Yes(19) No(10)
• sqrt3 :8
  triangle area=sqrt3/4*a^2
  square area=2a^2
• 11 years agoHelpfull: Yes(5) No(9)
• diagonal of a square is 2a
  area of the square=1/2*(diagonal)^2 i.e 2a^2
  side of the equi triangle is a
  area of equi triangle=(3/4)a^2
  3/4a^2:2a^2
  3:8
• 11 years agoHelpfull: Yes(5) No(18)
• Let the side of equilateral triangle = 1 unit.
  We know that area of an equilateral triangle =root3/a^2
  As side = 1 unit area of the equilateral triangle =root3/4
  Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
  We know that area of the square =half D^2 where D = diagonal
  So area of the square =half * 2^2=2
  Ratio of the areas of equilateral triangle and square = (root3/4):(2)
  =root3 :8
• 9 years agoHelpfull: Yes(2) No(0)
• √3/4*(a)^2:1/2*(2a)^2
  Thus √3:8
• 8 years agoHelpfull: Yes(1) No(0)
• area of equilateral triangle is sqrt3/4a^2
  assume side of equilateral triangle be 3
  thus diagonal of square is 6
  area of equialteral triangle is 9*sqrt3/4
  area of square is 1/2*diagonal^2=18
  9*sqrt3/4:18
  sqrt3/4:2
  sqrt3:8
  option a is the answer
• 8 years agoHelpfull: Yes(1) No(0)
• diagnol of a square=sqt2*a
  let "b" be the side of equilateral triangle
  therefore, sqrt2*a=2*b ==>a=sqrt b
  therfore : area of equilateral triangle/area of square=sqrt3 :8 is the final answer
  
• 8 years agoHelpfull: Yes(1) No(0)
• (a) is correct option
  ans = sqrt(3) a^2 / 2 a^2
  = sqrt(3)/8
• 7 years agoHelpfull: Yes(1) No(0)
• assume side of square is x1 and side of equilateral triangle is x2
  diagonal of the square is square root of 2(x1)
  sqrt(2)(x1)=2(x2)
  (3)^(12)4(x2)^2:x2^2
  substitute x2 value in terms of x1
  and the answer is 'a'
  
• 7 years agoHelpfull: Yes(0) No(0)
• The length of a diagonal of a square is a*sqrt(2) , where a= side of a square
  According to the question, the diagonal of a square is twice the side of equilateral triangle
  therefore, The side of this triangle is half of a*sqrt(2)
  So, Area of a Equilateral Triangle is {sqrt(3)/4} * (a/sqrt(2))^2
  
  ratio is -----> {sqrt(3)/4} * (a/sqrt(2))^2 : a^2
  => sqrt(3)/8 : 1
  => sqrt(3) : 8 (answer is option a)
• 1 year agoHelpfull: Yes(0) No(0)