Area Of Triangle #3
Geometry
Level
2
ABC is a Triangle with sides AB=2x, BC=x^3, AC=x^2 . . . . . . . . .
Angle B=2y, Angle C=y . . . . . . . . .
Find the Area Of Triangle ABC.
2.828
2.646
2.449
None Of These
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1 solution
The answer is None Of These. Because the triangle is not possible.
By Sine Rule:
2X/sin Y=x^2/sin 2Y, we get
cos Y=X/4. . . . . . . . . . eq. 1
By Cosine Rule:
cos Y= (X^4+X^2-4)/2X^3 . . . . . . . . eq. 2
So, eq.1 = eq. 2 . . . .
=> X^4+2X^2-8=0 . . . . . . . .
we get, X^2= 2 . . . . .
X= sqrt 2. . . .
But, the side opposite to the greater angle is greater.....
So, X^2 > 2X. . . . .
X > 2. . . . . . . . . .
But X= sqrt 2. . . . . . . . .
So, the triangle is not possible. . . . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!