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  • Write the correct answer in each of the following: The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is (A) an acute angled triangle (B) an obtuse angled triangle (C) a right triangle (D) an isosceles triangle

Write the correct answer in each of the following: The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is

(A) an acute angled triangle

(B) an obtuse angled triangle

(C) a right triangle  

(D) an isosceles triangle

Answers (1)

Answer: (A) an acute angled triangle

Solution.

Given: The ratio of angles of triangles is 5 : 3 : 7

Let angles of the triangle be \angle A,\angle B  and  \angle C

\angle A : \angle B : \angle C

5: 3 : 75x: 3x : 7x   \text{ here x = constant }

Then, \angle A = 5x

   \angle B = 3x

   \angle C = 7x

In \triangle ABC

\angle A + \angle B + \angle C = 180^{\circ}

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

15x = 180^{\circ}

x=\frac{180}{18}=12^{\circ}

\angle A = 5x = 5\times 12^{\circ}= 60^{\circ}

\angle B = 3x = 3 \times 12^{\circ} = 36^{\circ}

\angle C = 7x = 7 \times 12^{\circ} = 84^{\circ}

All angles are less than 90° hence acute.

Posted by

infoexpert26

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