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Mathematics

Assertion (A): A triangle with sides 2 cm, 3 cm, 4 cm is not a right angled triangle.

Reason (R): A triangle with sides 2 cm, 3 cm, 4 cm is a scalene triangle.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Pythagoras Theorem

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Answer

Given the sides: a = 2 cm, b = 3 cm, c = 4 cm.

The longest side is c = 4 cm.

Let's check if c2 = a2 + b2

Taking L.H.S.,

c2 = 42 = 16.

Taking R.H.S.,

a2 + b2 = 22 + 32

= 4 + 9

= 13.

Since 16 ≠ 13, the condition for a right-angled triangle is not met.

Therefore, the triangle with sides 2 cm, 3 cm, 4 cm is not a right-angled triangle.

∴ Assertion (A) is true.

A scalene triangle is defined as a triangle in which all three sides have different lengths.

Given the side lengths are 2 cm, 3 cm, and 4 cm. All three lengths are distinct.

∴ Reason (R) is true.

∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Hence, option 4 is the correct option.

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