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Question

The perimeter of an isosceles triangle is 32 cm and its base is 12 cm and one of its equal sides form the diagonals of a paralleleogram. Find the area of the paralleleogram. 


Solution

The perimeter of the triangle = 2x + b = 32 cm
= 2x + 12 = 32
= 2x = 32 - 12 
= 2x = 20
= x = 20/2
= x = 10 cm
Therefore, the height of isosceles triangle is h.
Then, Applying Pythagoras theorem 
= (h)2 = (x)2 - (b/2)2
= (h)2 = (10)2 - (12/2)2
= (h)2 = 100 - 36
= (h)2 = 64
= h = 8 cm
Area of triangle = h x b/2
= 8 x 12/2
= 96/2
= 48 cm2

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