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Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Integer Value Correct Type

Q. 1. Let ABC and ABC' be two non-congruent 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.

Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Applying sine law in Δ ABC', we get

Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
So, the required area = ar (ΔABC) - ar (ΔABC')

Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


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 r2 is equal to

Ans. 3

Solution. 

Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

⇒  C = 120° as C is obtuse angle.

Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

The document Integer Answer Type Questions: Properties of Triangle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is a part of the JEE Course Maths 35 Years JEE Main & Advanced Past year Papers.
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