An equilateral triangle is inscribed in a square. The length of each side of the triangle is equal to half the length of the diagonals of the square. Find the ratio of the areas of the triangle to that of the square.
a) sqrt(3)/8
b) sqrt(5)/8
c) 8/sqrt(3)
d) 8/sqrt(5)

• ans is (a)
  
  length of side of triangle =1/2 diagonal of square
  so diagonal =2(side)of triangle
  let side be a
  so diagonal=2a
  now area of eqiulateral triangle =sqroot(3)/4 x side*2
  so ratio becomes root(3)/4 x side*2 / .5x diagonal*2
  solving this we get sqroot(3)/8
• 9 years agoHelpfull: Yes(9) No(0)
• let side of triangle= a
  than diagonal of square = 2a
  
  area of equi. tri. = sqrt(3)/4 * a^2
  area of square whose diagonal is d = 1/2 d^2
  here area of square = 1/2 * (2a)^2= 2a^2
  
  area of tri./ area of sqr. = (sqrt(3)/4 * a^2)/ 2a^2 = sqrt(3)/8
  
  thus ans is (a)
• 9 years agoHelpfull: Yes(1) No(0)
• Area of triangle: Area of the square
  sqrt(3)a^2/4: a^2 and the length of each side of the triangle=a/sqrt(2)
  sqrt(3)/4 *(a/sqrt(2))^2 : a^2
  sqrt(3)/8:1
  sqrt(3)/8
  
  
• 8 years agoHelpfull: Yes(0) No(0)