In a rhombus LMNO, ZM = 60° and LM = 14 cm. Find the diagonal LN ?
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Given : a rhombus LMNO,
∠M = 60° and LM = 14 cm
To Find : Diagonal LN
Solution:
A rhombus has all 4 sides equal
Hence LM = MN = 14 cm
LN = ?
∠M = 60°
Cosine law : a² + b² - c² = 2abcosC
=> 14² + 14² - LN² = 2(14)(14)Cos60°
=> 14² + 14² + LN² = 14²
=> LN² = 14²
=> LN = 14
Another way
ΔLMN
LM = MN and ∠M = 60°
Hence all three angles of triangle are 60°
so ΔLMN is an equilateral triangle
=> LN = LM = MN
Hence LN = 14 cm
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