From a point within an equilateral triangle, perpendiculars are drawn to the three sides and are 3, 7 and 11 cm in length. Then the perimeter of the triangle (in cm) is

a. 42√3
b. 21√2
c. 21
d. 7

• Taking 3 perpendiculars within the triangle from the same point and joining that point to the corners of the triangle, makes three triangles within the equilateral triangle.
  
  Given the sides of the perpendicular as 3cm, 7cm and 11cm.
  
  Let the side of the equilateral triangle be a
  
  Then,
  
  Area of the equilateral triangle = (3^(1/2)*(a^2))/4
  
  So √3a^2/4 = 1/2*3*a + 1/2*7*a + 1/2*11*a
  = 1/2(21a)
  = 21a/2
  => a = 42/√3
  => 3a = 42*√3
  
  Thus, the perimeter of the triangle is 42√3 cm.
• 11 years agoHelpfull: Yes(45) No(0)
• area of equilateral triangle is(root(3)/4)a^2.............................................................(eq1)....and area due to these three triangle formed within the equilateral triangle is ((1/2)*3*a)+((1/2)*7*a)+((1/2)*11*a)..................(eq2)...........equating eq1 and eq2 we get....42/(root(2))
• 11 years agoHelpfull: Yes(2) No(4)
• 42..is it correct
  
• 11 years agoHelpfull: Yes(0) No(3)
• area of the eq.triangl=root3/4=x ^2.....eq(1)
  the perpendiculars cut the side into two equal parts,therefore area=1/2*3x+1/2*7x+1/2*11x....eq(2)
  equalize 1&2..;we get
  root3/4*x^2=1/2*3x+1/2*7x+1/2*11x
  a=42/root3.
  perimeter of the triangle=3x=3*42/root3
  =42*root3
• 11 years agoHelpfull: Yes(0) No(0)