The angles of a triangle are in the ration 3 : 5 : 7. The triangle is

Question:

The angles of a triangle are in the ration 3 : 5 : 7. The triangle is
(a) acute-angled
(b) obtuse-angled
(c) right-angled
(d) an isosceles triangle

 

Solution:

(a) acute-angled

Let the angles measure $(3 x)^{\circ},(5 x)^{\circ}$ and $(7 x)^{\circ}$.

Then,

$3 x+5 x+7 x=180^{\circ}$

$\Rightarrow 15 x=180^{\circ}$

$\Rightarrow x=12^{\circ}$

Therefore, the angles are $3(12)^{\circ}=\mathbf{3 6}^{\circ}, 5(12)^{\circ}=\mathbf{6 0}^{\circ}$ and $7(12)^{\circ}=\mathbf{8 4}^{\circ}$.

Hence, the triangle is acute-angled.

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