Question

The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y where x, y > 0 then the triangle is ______.

Options

• right angled

• obtuse angled

• equilateral

• none of these

Answer 1

The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y where x, y > 0 then the triangle is obtuse angled.

Explanation:

Let a = 3x + 4y, b = 4x + 3y and c = 5x + 5y

as x, y > 0, c = 5x + 5y is the largest side

∴ C is the largest angle.

Now, cos C = `(a^2 + b^2 - c^2)/(2ab)`

cos C = `((3x + 4y)^2 + (4x + 3y)^2 - (5x + 5y)^2)/(2(3x + 4y)(4x + 3y))`

= `(-2xy)/(2(3x + 4y)(4x + 3y)) < 0`

∴ C is obtuse angle `\implies` ΔABC is obtuse angled