Item contains a Question followed by two Statements. Answer each item using the following instructions : 

The lengths of two longer sides of the triangle Δ are 25 cm and 24 cm.  

Question: What is the length of the shortest side ? 

Statement I: The angles of Δ  are in the ratio 1 : 2 : 3.  

Statement II: The length of the perpendicular drawn on the longest side of Δ from its opposite vertex is 6.72 cm.  

Concept:

1) If in a right-angle triangle

Ratio of three angle = 30° : 60° : 90°  (or 1 : 2 : 3), then

The ratio of it's side opposite to this angle = 1: √3 : 2

2) AC × BD = AB × AD 

Calculation:

Statement I:

The angles of Δ are in the ratio 1 : 2 : 3

As we know in a triangle sum of all the angles is 180°

So, The angles of Δ are 30°, 60°, 90°

Therefore,

So, the sides should be in the ratio 1: √3 : 2

By using the Pythagoras' theorem

x2 + 242 = 252

⇒ x2 + 576 = 625

⇒ x2 = 625 - 576

⇒ x2 = 49

⇒ x = 7

So, the shortest side = 7 cm

But, 7, 24 & 25 are not in the ratio 1 : √3 : 2, but as per the property,

If the ratio of angle = 1 : 2 : 3 then the ratio of side = 1 : √3 : 2. 

Therefore, the information given in Statement I is not sufficient. 

Statement II:

From the Pythagoras theorem, we got x = 7 

By using the above property

BC × AD = AB × AC

7 × 24 = 25 × AD

AD = 168/25 = 6.72

Therefore, if we take the length of the shortest side equal to 7 cm, we got the length of the perpendicular drawn on the longest side of Δ from its opposite vertex is 6.72 cm.  

Statement 2 is sufficient to answer this question.

∴ Option (1) is correct.