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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