NIMCET 2013 Question Paper with solutions

Question : 29 of 120

Marks: +1, -0

In a Δ ABC , (c + a + b) (a + b - c) = ab. The measure ofthe angle C is :

Solution:

∵(a+b)^2-c^2=ab

⇒

a^2+b^2+2ab-c^2=ab

⇒a^2+b^2+ab-c^2=0

⇒a^2+b^2-c^2=-ab

∴\cos\;c={a^2+b^2-c^2}/{2ab}

⇒\cos\;c={-ab}/{2ab}={-1}/2⇒c={2π}/3

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