In a right-angle triangle ABC, with a right angle at 'B', 'D' is the midpoint of AB and DE is a perpendicular drawn on side AC. If AB = 20 cm and BC = 15 cm, then find the area of ∆AED (in cm²).
Show answer & explanation
Correct answer: C
Explanation
ΔAED and ΔABC are similar by the AA criterion (∠A is common, ∠AED = ∠ABC = 90°)
Hypotenuse AC = √(20² + 15²) = 25 cm
Midpoint D ⇒ AD = 20 ÷ 2 = 10 cm
Side ratio (AD/AC) = 10/25 = 2/5
Area ratio = (2/5)² = 4/25
Area of ΔABC = 1/2 × 20 × 15 = 150 cm²
Area of ΔAED = 150 × 4/25 = 24 cm²