In a parallelogram, the lengths of the two adjacent sides are 12 cm
and 14 cm respectively. If the length of one diagonal is 16 cm, find
the length of the other diagonal.
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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
<ABC = arc cos 0.25 = 75.52248781 deg = <CDA
<BCD = <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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