1.

In a parallelogram, the lengths of the two adjacent sides are 12 cmand 14 cm respectively. If the length of one diagonal is 16 cm, findthe length of the other diagonal.​

Answer»

Answer;-

ABCD is a parallelogram with AB = 12 cm, BC = 14 cm and AC = 16 cm, we need to find out BD.

In triangle ABC, AB = 12 cm, BC = 14 cm and AC = 16 cm

AC^2 = AB^2 + BC^2 -2*AB*BC COS ABC, or

16^2 = 12^2 + 14^2 - 2*12*14 cos ABC, or

256 = 144 + 196 - 336 cos ABC, or

336 cos ABC = 144+196–256 = 84, or

cos ABC = 84/336 = 0.25, or

BAD = 180 - 75.52248781 = 104.4775122 deg

Applying cosine formula to triangles ABD and BCD

BD^2 = AB^2 + DA^2 -2*AB*DA cos BAD

= 12^2 + 14^2 - 2*12*14 cos 104.4775122

= 144 + 196 - 336 cos 104.4775122

= 340 + 84

= 424, or

BD = 20.29126028 cm.


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