The question cons A. Both Assertion (A) and Reason (B) are true and Reason (R) is a correct explanation of Assertion (A).

B. Both Assertion (A) and Reason (B) are true but Reason (R) is not a correct explanation of Assertion (A).

C. Assertion (A) is true and Reason (R) is false.

D. Assertion (a) is false and Reason (R) is true.

In the given question,

Let us assume the sides of the triangle be 2x, 3x and 4x

We know that,

Perimeter of triangle = Sum of all sides

36 = 2x + 3x + 4x

36 = 9x

x =

x = 4

∴ Sides of the triangle are:

2x = 2 × 4 = 8 cm

3x = 3 × 4 = 12 cm

4x = 4 × 4 = 16 cm

Let, a = 8 cm, b = 12 cm and c = 16 cm

So, s =

=

=

= 18 cm

Now, by using Heron’s formula we have:

Area of triangle =

=

=

=

= 6 × 2

= 12 cm²

Also, if 2s = (a + b + c)

Where a, b and c are the sides of the triangle then:

Area = which is false as it should be:

Area =

∴ Assertion is true whereas reason is false

Hence, option (c) is correct