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Comprehension

ABC is a triangle right-angled at A. Further,
AB = 8 cm, BC = 10 cm. D is the point on BC such that AD is perpendicular to BC.

What is AD equal to?

This question was previously asked in
UPSC CDS-I 2025 (Elementary Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 4·8 cm
  2. 5·0 cm
  3. 5·2 cm
  4. 5·4 cm

Answer (Detailed Solution Below)

Option 1 : 4·8 cm
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Detailed Solution

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Given:

The triangle ABC is right-angled at A.

AB = 8 cm, BC = 10 cm,

D is perpendicular to BC.

Calculation:

AC2 = BC2 - AB2

AC = √(100 - 64)

AC = √36 = 6 cm  

qImage685ed9d6bf40c16fd70fd5e4

AD = (AB × AC)/(BC)

AD = (6 × 8)/10 = 4.8 cm

∴ The correct answer is option 1.

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