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Integer Value Correct Type
Q. 1. Let ABC and ABC' be two noncongruent triangles with sides AB = 4, AC = AC' = 2√2 and angle B = 30°. The absolute value of the difference between the areas of these triangles is
Ans. 4
Solution. Let ∠ACC' = θ , then ∠AC'C = θ (∴ AC = AC') and ∠AC' B = 180  θ.
Applying sine law in Δ ABC', we get
So, the required area = ar (ΔABC)  ar (ΔABC')
Q. 2. Consider a triangle ABC and let a , b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3 , if ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r^{2} is equal to
Ans. 3
Solution.
⇒ C = 120° as C is obtuse angle.
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