Let ABC be a right-angled triangle such that ∠C = 90°. Let D be a point on AB such that CD is perpendicular to AB. If AC = 5 cm and BC = 12 cm, find the length of CD (in cm).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. .
Area of △ABC = (1/2) × AC × BC = (1/2) × 5 × 12 = 30 cm2
AB = √(AC2 + BC2) = √(52 + 122) = √169 = 13 cm
Area of △ABC = (1/2) × AB × CD = 30
⇒ 13 × CD = 60
⇒ CD = 60/13