The altitude drawn to the base of an isosceles triangle is 8 cm an its perimeter is 64 cm. what is the area of the triangle ?

• let two equal sides are x cm & base = 2y cm
  
  perimeter = 64
  => x+x+2y = 64
  => x+y=32 ----(1)
  
  given, h = 8 cm
  altitude divides base in two equal parts
  x^2 = 8^2 + y^2
  => x^2 - y^2 = 64
  => (x+y)*(x-y)=64
  => 32*(x-y) = 64 [from,(1)]
  => x - y = 2 -----(2)
  
  from(1)& (2)
  x=17,y=15
  
  area of the triangle = (1/2)* 2y * h = y*h = 15*8 = 120 cm^2
• 10 years agoHelpfull: Yes(4) No(1)