The sides of a triangle are in the ratio 4 âˆ¶ 6 âˆ¶ 8. The triangle is a/an :

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)
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  1. isosceles triangle
  2. obtuse-angled
  3. acute-angled
  4. right-angled

Answer (Detailed Solution Below)

Option 2 : obtuse-angled
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Detailed Solution

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Given:

The sides of a triangle are in the ratio 4 âˆ¶ 6 âˆ¶ 8. 

Concept used:

The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side.

Calculation:

Let the sides of the triangle be 4x, 6x, and 8x respectively.

Now,

(4x)2 + (6x)2 < (8x)2

⇒ 52x2 < 64x2

So, the triangle is an obtuse-angled triangle.

∴ The triangle is obtuse-angled.

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