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Question

A rhombus of side 20cm has two angles of 60 each .Find the length of the diagonal.


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Solution

Step-1: length of the diagonal of AC:

The diagonals of a rhombus bisect each other at a right angle.

AOD=90°

Find the length of diagonal AC:

InrightangleAODsin30°=OAAD12=OA20[sin30°=12]OA=202OA=10cm

Since the diagonal of the rhombus bisect each other,

AC=2·OAAC=2×10AC=20cm

Step-2: length of the diagonal of BD:

Find the length of the diagonal BD:

InrightangleAODcos30°=ODAD32=OD20[cos30°=32]OD=2032OD=103cm

Since the diagonal of the rhombus bisect each other,

BD=2·ODBD=2×103BD=203cm

Hence, the diagonals are AC=20cm,BD=203cm.


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