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If x, y gt 0, then prove that the triang...

If x, `y gt 0`, then prove that the triangle whose sides are given by `3x + 4y, 4x + 3y, and 5x + 5y` units is obtuse angled.

Text Solution

Verified by Experts

Let `a = 3x + 4y, b = 4x + 3y and c = 5x + 5y`
Obviously, c is the greatest side, hence `angle C` is the greatest angle
Thus,
`cos C= (a^(2) + b^(2) - c^(2))/(2ab)`
`= (-2xy)/(2(12 x^(2) + 25 xy + 12y^(2)) lt 0`
since `cos C lt 0, anlge C gt pi//2`. So, triangle is obtuse angled
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