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Given a ABC in which

I. A, B and C are in the ratio 3: 2 :1.

II. AB , AC and BC are in the ratio 3 : 3 : 2 3 and AB = 3 3 cm.

Is ABC a right triangle?

The question give above has two Statements I and II. Answer the questions by using instructions given below:

(a) If the question can be answered by one of the given statements only and not by the other.

(b) If the question can be answered by using either statement alone.

(c) If the question can be answered by using both the statements but cannot be answered by using either statement.

(d) If the question cannot be answered even by using both the statements together.

I. It is given in the question that,

∠A, ∠B and ∠C are in the ratio 3: 2: 1

Let ∠A = 3x

∠B = 2x

∠C = x

We know that, sum of angles of a triangle = 180^{o}

∠A + ∠B + ∠C = 180^{o}

3x + 2x + x = 180^{o}

6x = 180^{o}

x =

x = 30^{o}

Hence, ∠A = 3 × 30^{o} = 90^{o}

∴ is a right-angled triangle

II. It is also given that:

AB, AC and BC are in the ratio 3: √3: 2√3

Now, AB = 3x, AC = and BC = 2√3x

As it is given that,

AB = 3√3

∴ x = √3

AC = 3

BC = 6

Now, by using Pythagoras theorem in we get:

AC =

3 =

3 =

3 ≠ √63

∴ The question can be answered by using either statement alone

Hence, option (b) is correct

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