The perimeter of an isosceles triangle is 64 cm. The ratio of the equal side to its base is 5 : 6. Find the area of the triangle.


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Answer:

192 cm2

Step by Step Explanation:
  1. Let's assume, the lengths of the base and the equal sides of the isosceles triangle are b cm and x cm respectively.
    Following figure shows the isosceles triangle ABC,

    The ratio of the equal side to its base is 5 : 6.
    Therefore,  
    5
    6
      =  
    x
    b
     
    By cross multiplying, we get:
    b =  
    6x
    5
      ------(1)
  2. According to the question, the perimeter of the isosceles triangle ABC = 64 cm
    Therefore, x + x + b = 64
    ⇒ 2x +  
    6x
    5
      = 64  [From equation (1), b =  
    6x
    5
     ]
    ⇒  
    10x + 6x
    5
      = 64
    ⇒ 10x + 6x = 320
    ⇒ 16x = 320
    ⇒ x = 20 cm
  3. Putting the value of x in equation (1), we get:
    b =  
    120
    5
      = 24 cm
  4. The area of the isosceles triangle ABC can be calculated using Heron's formula, since all sides of the triangle are known.
    S =  
    64
    2
      = 32 cm
    The area of the isosceles triangle ABC = √S(S - AB)(S - BC)(S - CA)
    = √32(32 - 24)(32 - 20)(32 - 20)
    = 192 cm2
  5. Thus, the area of the triangle is 192 cm2.

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