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