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.?

Only I
Only II
Only III
Either I or II
Either II or III

LohaHridoy

9 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : 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.

9 views Answered 2022-09-04 04:29

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