The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

The sides of the triangle ABC are in the ratio 2 : 3 : 4 and its perimeter is 36 cm. Then ar(Δ ABC) = cm².

If 2s = (a + b +c) where a, b, c are the sides of the triangle, then its area is = .

Question

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

Assertion (A)	Reason (R)
The sides of the triangle ABC are in the ratio 2 : 3 : 4 and its perimeter is 36 cm. Then ar(Δ ABC) = cm².	If 2s = (a + b +c) where a, b, c are the sides of the triangle, then its area is = .

Philoid · Accepted Answer

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