ABCD is a parallelogram. its perimeter is 20 cm. if (^ABD)=60, BD=8 CM, calculate AB, AD.

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We are given a parallelogram ABCD with a perimeter of 20 cm. The side BD = 8 cm and angle ABD= 60 degrees.

As ABCD is a parallelogram AB = CD and AD = BC

The perimeter of the parallelogram is AB + BC + CD + DA = 20 cm

=> AB + AD = 20/2 = 10 cm

If AB = x, AD = 10 - x

BD = 8 cm

Apply the cosine rule to triangle ABD

AB^2 + BD^2 - 2*AB*BD*cos ABD = AD^2

x^2 + 8^2 - 2*x*8*cos 60 = (10 - x)^2

=> x^2 + 64 - 8x = 100 + x^2 - 20x

=> 12x = 36

=> x = 36/12 = 3

This gives AB = 3 cm and AD = 7 cm.

Approved by eNotes Editorial Team
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