5. Perimeter of a equilateral triangle is equal to the perimeter of Hexagon. What is the ratio of their areas?
a. 6:1
b. 1:6
c. 3:2
d. 2:3

• let side of eq. triangle be x & side of hexagon be y then
  
  Perimeter of a eq. triangle = perimeter of Hexagon => 3x=6y => x= 2y
  
  area of eq. triangle (√3/4) * x^2
  ---------------------- = ------------------- = 2/3 = 2:3 [put x=2y]
  area of hexagon 6* (√3/4)* y^2
  
  d. 2:3
  
• 10 years agoHelpfull: Yes(34) No(2)
• let side of eq. triangle be x & side of hexagon be y then
  
  Perimeter of a eq. triangle = perimeter of Hexagon => 3x=6y => x= 2y
  
  area of eq. triangle (√3/4) * x^2 (2y)^2
  ---------------------- = ------------------- = --------- = 2/3 = 2:3 [put x=2y]
  area of hexagon 6* (√3/4)* y^2 6* y^2
  
  d. 2:3
• 10 years agoHelpfull: Yes(7) No(0)
• Let the side of the triangle be x and that of the hexagon be y.
  Given, 3x=6y
  =>y=(1/2)x
  Now, area of the equilateral triangle is 3^(1/2)/4*(x^2)
  Also, the area of the hexagon is divided into 6 equilateral triangles of equal side
  Hence, area of the hexagon with side y= 3^(1/2)/4*(y^2)*6
  The ratio of the areas is:
  3^(1/2)/4*(x^2):3^(1/2)/4*(y^2)*6
  => x^2:6*(y^2)
  => x^2:6*[(1/2)^2]*(x^2)
  => 1:6*(1/4)
  => 2:3
  Hence the answer is d. 2:3
• 10 years agoHelpfull: Yes(2) No(0)
• area of equilateral triangle=√(3)*a1^2/4
  area of hexagon=6*area of each equilateral triangle=6*(√(3)*a1^2/4)
  we know that perimeters are equal...3a1=6a2..a1=2a2.
  taking the ratios of areas..(a1)^2/(6*(a2^2))=2/3..
  so option (d) is correct
• 10 years agoHelpfull: Yes(2) No(0)
• answer is c)3:2 => check the link below for explanation
  http://mathcentral.uregina.ca/QQ/database/QQ.02.06/trevor1.html
• 10 years agoHelpfull: Yes(2) No(0)
• b. 1:6
  let side of hexagon= x
  perimeter of hexagon= 6x
  and perimeter of equilateral triangle = 3*side
  as both the perimeters are equal
  So, 3*side=6x
  therefore side of triangle= 2x
  area of triangle= [(3^1/2)/4]*a^2
  and area of hexagon= [[(3^1/2)/4]*a^2]*6
• 10 years agoHelpfull: Yes(1) No(2)