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Mathematics

Assertion (A): Heron's formula can be used to find the area of a scalene triangle only.

Reason (R): If ABC is a triangle with side a, b and c respectively, then its area = s(s−a)(s−b)(s−c)\sqrt{s(s - a)(s - b)(s - c)}, where s = a+b+c2\dfrac{a + b + c}{2}.

  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).

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Answer

With the help of heron's formula, we can find the area of any triangle and not particularly scalene triangle.

∴ Assertion (A) is false.

If ABC is a triangle with side a, b and c respectively, then its area = s(s−a)(s−b)(s−c)\sqrt{s(s - a)(s - b)(s - c)}, where s = a+b+c2\dfrac{a + b + c}{2}.

This is the correct definition and formula for Heron's formula. The variable 's' represents the semi-perimeter of the triangle.

∴ Reason (R) is true.

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

Hence, option 2 is the correct option.

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