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The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Perpendicular and base of a right-angle triangle are 5x and 12x respectively. Find the area of right-angled triangle. I. Perimeter of the right-angle triangle is p cm.  II. Length of the diagonal side is d cm. III. Area of another triangle similar to the given triangle is 300 cm2.

The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Perpendicular and base of a right-angle triangle are 5x and 12x respectively. Find the area of right-angled triangle. I. Perimeter of the right-angle triangle is p cm.  II. Length of the diagonal side is d cm. III. Area of another triangle similar to the given triangle is 300 cm2. Correct Answer Either I or II

Perpendicular = 5x

Base = 12x 
Applying Pythagoras theorem: 

(5x)2 + (12x)2 = d2

25x2 + 144x2 = 169x2 = d2
13x = d 
From statement I: 
Perimeter (p) = 5x + 12x + 13x = 30x 
⇒ x = p/30 
Area = 1/2 × base × perpendicular = 1/2 × 5x × 12x = 30x2 = p2/30 
From statement II:
Length of diagonal ⇒ d = 13x/2 
⇒ x = 2d/13 
Area = 1/2 × base × perpendicular = 1/2 × 5x × 12x = 30x2 = 30 × 2d/13 × 2d/13 
= 120d2/169 

From statement III:

If ratio of corresponding sides is not given, we cannot establish relation between their area.
∴ We can find area from statement I and II but not from III.

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