ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8 cm. AD is perpendicular to BC. What is the area (in cm2) of triangle ABD ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6.
AB = 5 cm, AC = √41 cm and BC = 8 cm
Applying cos theorem;
CosB = (52 + 82 – 41)/(2 × 5 × 8) = 3/5
Now in triangle ABD;
AB = 5 cm & CosB = 3/5
∴ BD = 5 × 3/5 = 3 cm
∴ AD = 4 cm (Pythagoras theorem)
∴ Area of triangle ABD = ½ × 4 × 3 = 6 cm2