A square and an equilateral triangle have same perimaters. If the diagonal of the square is 12 sqrt 2 cm then what is the area of the triangle ?

• When 'a' is the side of a square then its diagonal is a*sqrt(2).
  
  Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.
  
  Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm
  
  Side of triangle = perimeter/3 = 48/3 = 16cm
  
  Area of equilateral triangle = sqrt(3)/4*(side of triangle)^2 = sqrt(3)/4*16^2
  = sqrt(3)/4*256 = 64*sqrt(3) sq.cm.(ans)
• 12 years agoHelpfull: Yes(6) No(1)
• When 'a' is the side of a square then its diagonal is a*sqrt(2).
  
  Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.
  
  Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm
  
  Side of triangle = perimeter/3 = 48/3 = 16cm
  
  Altitude of equilateral triangle = sqrt(3)/2*side of triangle sqrt(3)/2*16 = 8*sqrt(3) cm
  
  Area of triangle = (1/2)*16*8*sqrt(3) = 64*sqrt(3) sq.cm.(ans)
• 12 years agoHelpfull: Yes(2) No(0)
• if diagonal of a square is a*sqrt(2) means then side is a.
  therefore, the side of the square is 12 cm. area of the triangle is a^2*(sqrt(3)/4). so answer is 64sqrt(3) sq.cm.
• 10 years agoHelpfull: Yes(2) No(0)
• When 'a' is the side of a square then its diagonal is a*sqrt(2).
  
  Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.
  
  Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm
  
  Side of triangle = perimeter/3 = 48/3 = 16cm
  
  Altitude of equilateral triangle = 1/2*side of triangle =(1/2)*16 = 8cm
  
  Area of triangle = (1/2)*16*8 = 64 sq.cm.(ans)
• 12 years agoHelpfull: Yes(1) No(3)
• When 'a' is the side of a square then its diagonal is a*sqrt(2).
  
  Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.
  
  Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm
  
  Side of triangle = perimeter/3 = 48/3 = 16cm
  
  Area of equilateral triangle = sqrt(3)/4*(side of triangle)^2 = sqrt(3)/4*16^2
  = sqrt(3)/4*256 = 64*sqrt(3) sq.cm.(ans)
• 12 years agoHelpfull: Yes(1) No(0)
• 20/100=0.2
  0.2*20=4
• 10 years agoHelpfull: Yes(1) No(0)
• PERIMETER OF SQUARE=PERIMETER OF EQ.TRIANGLE
  4A=3L. DIAGONAL 0F SQUARE=12SQ.RT2=SQ.RT(A^2+A^2)
  SQ.RT(2)A=12.SQ.RT(2)=>A=12. PERIMETER OF STRIANGLE=48.L=16.
  AREA OF TRIANGLE=1/2(B*H)=(1/2)*16*(SQ.RT(432))
• 12 years agoHelpfull: Yes(0) No(2)
• a=12
  perimeter of square=48
  therefore side of traingle is 16
  area of traingle is 1.732 *64 cm^2
• 11 years agoHelpfull: Yes(0) No(0)
• When 'a' is the side of a square then its diagonal is a*sqrt(2).
  
  Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.
  
  Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm
  
  Side of triangle = perimeter/3 = 48/3 = 16cm
  
  Altitude of equilateral triangle = sqrt(3)/2*side of triangle sqrt(3)/2*16 = 8*sqrt(3) cm
  
  Area of triangle = (1/2)*16*8*sqrt(3) = 64*sqrt(3) sq.cm.(ans)
• 11 years agoHelpfull: Yes(0) No(0)
• 144 cm^2.
  area(triangle)=area(square)
  diagonal of square=12 sqrt 2=(side length) sqrt 2
  i.e,side length of square=12 cm
  so area of square=12^2=144 cm^2=area(triangle)
• 10 years agoHelpfull: Yes(0) No(0)
• let side of square & triangle be a and b resp.
  A.T.Q , 4a=3b
  diagonal of square=a*sqrt(2) which is given as 12*sqrt(2)
  so, a=12 => b=16
  so, area of triangle equals sqrt(3)*16*16/4=64*sqrt(3) sq.cm (ans)
  
• 10 years agoHelpfull: Yes(0) No(0)
• Answer will be 36^1/2
• 10 years agoHelpfull: Yes(0) No(1)