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Question
The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is ______.
Options
an acute angled triangle
an obtuse angled triangle
a right triangle
an isosceles triangle
Solution
The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is an acute angled triangle.
Explanation:
Let the angle of the triangle are 5x, 3x and 7x.
As we know that sum of all angle of triangle is 180°.
Now, 5x + 3x + 7x = 180°
15x = 180°
x = `(180^circ)/15`
x = 12°
Hence, the angle of the triangle are:
5 × 12° = 60°
3 × 12° = 36°
7 × 12° = 84°
All the angle of this triangle is less than 90 degree.
Hence, the triangle is an acute angled triangle.
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