Question to Find Area of Triangle

Topic : Area of Triangle
Question: In any ∆ ABC a²Sin2B+b²Sin2C =
A) Area of the triangle
B) Twice the Area of the triangle
C) Thrice the Area of the triangle
D) Four times of the Area of the triangle

Solution :
In the data any triangle is mentioned.
Therefore let us take equilateral triangle having side 1 unit.
That is a=b=c=1, A=B=C=60º.
Area of the equilateral triangle is = [(√3)/4]a²=[(√3)/4]x1=(√3)/4.
value of the expression given =1²xSin120+1²xsin120=[(√3)/2]+[(√3)/2]= √3------(1)

Option A): Area of the Triangle=(√3)/4, but value of expression = √3 These two are not equal. Hence Option A is not correct
Option B): Twice the Area of the triangle=2x[(√3)/4]=(√3)/2, but the value of expression is √3. Hence option B is incorrect
Option C):Thrice the Area of the triangle = 3x[(√3)/4], but the value of the expression is √3. hence option C also incorrect.
Option D): Four times of the Area of the triangle=4x[(√3)/4]= √3, this is also equal to the value of the expression shown in ---(1).

Hence Option D is the correct choice of the above question.


Hope the Answer and Explanation will be helpful for you.